The concept of time value of money is the basic premise of financial decisions. The concept of time value of money confers that the value of money reduces with the efflux of time. This means that the value of one dollar today will not be the same after 1 year from today (Drake and Fabozzi, 2009). The purchasing power of one dollar today will reduce over the period of time due to inflation and other economic changes. For example, a man who bought suppose one KG bananas in one dollar today would not be able to do so after one year. After one year he might has to pay 1.5 dollar to buy one kg bananas. The consideration of time value of money is of utmost importance in the financial decisions. If a firm deciding on to invest in a project does not consider the time value of money, it will end up evaluating the project’s financial viability in wrong way (Drake and Fabozzi, 2009).
There are four basic factors which lead the consideration of time value of money concept. These four factors are risk and uncertainty, inflation, consumption, and investment opportunity. It is important to consider the risk and uncertainty involved in an investment decision (Silver, 2011). As the future is uncertain and hence the receipt of cash flows can not be guaranteed with certainty, therefore, the firm makes provision for this uncertainty by adjusting the discount rate. The inflation refers to increase in the price of goods and services over the period of one year. The increase in the price of goods and services affects the cash flows of a firm and hence it is important to consider inflation when assessing financial viability of the project. The discount rate is further adjusted on account of inflation after being adjusted for risk and uncertainty (Silver, 2011).
Consumption and investment opportunity leads encourages a person to receive money today rather than tomorrow. The person would always prefer to consume today rather than consuming tomorrow. Further, the dollar money received today could be invested to earn income for the future (Halpin and Senior, 2011). Thus, a person receiving money in future would like have incentive or some extra charge. For example, a person receiving $100 today would not like to defer this payment for one year if he does not receive anything greater than $100. If the person defers the payment of $100 for one year, he would be deprived of consumption of goods or services which he could have availed by utilizing $100 today. He would also loose opportunity to invest money. So, he would be happy to defer it if say the payment after one year becomes $110. In such a case, there would be some incentive to the person deferring payment for one year (Halpin and Senior, 2011).
There are two techniques being emerged from the concept of time value of money namely discounting and compounding. Discounting refers to bringing the value of money to be received in future to the present times while compounding means determining the future value of money (Baker and English, 2011). An example of discounting technique:
Value of $100 receivable after one year at discount rate of 10% would be $90.90. This is arrived at as under:
PV = FV/(1+r)t
Here, PV = Present value
FV = Future value
R = Rate of discount
= 100/(1+.10)1
= 90.90
On the other hand, if we calculate let say value of $100 invested at the rate of 10% after one year, it would amount to $110, this is called compounded value. This value has been arrived at as under:
Fv = PV (1+r)n
= 100(1+.10)1
= $110
In capital budgeting decisions, the discounting technique is used instead of compounding. The discounting technique provides computation of the present value of future cash flows which is compared with the investment amount to arrive at the decision. The compounding technique in the capital budgeting decisions can not be applied as it would be difficult to determine the rate of return that the project would generate over the period of time. However, the future cash inflows can be estimated with reliability. With the help of discounting technique, the present value of the future cash flows can be determined (Shapiro, 2008).
It is to be noted that a discount rate is used in computing the present value of future cash flows. This discount rate is determined having regards to the investor’s desired rate of return (Shapiro, 2008). The discount rate could also be said to be the approximation to the cost of capital of the firm. A firm may use its weighted average cost of capital as the discount rate. The weighted average cost of capital of the firm comprises the cost of different components of the capital such as equity, debt, and preference shares. In an all equity firm, the CAPM return could also provide an approximation of the discount rate. However, whatever method is used in computing the discount rate, a further adjustment for the risk and inflation is required. The discount rate must incorporate risk and it should be adjusted for inflation. Further, it may be noted that the discount rate would change from project to project because of change in the risk of different projects (Shapiro, 2008).
There is immense use of the concept of time value of money in the valuation of the financial instruments. All the financial instruments such as equity shares, preferences shares, bonds and debentures are valued by discounting the future income flowing from the investment. The equity shares are valued with reference to the discounted value of expected dividend payments over the period (Shim and Siegel, 2008). According to the dividend discount model, the value of an equity share can be computed by the following formula:
po = D0*(1+g)/(Ke-g)
Where,
Do = Current dividend
Ke = Cost of equity
G = growth rate
Thus, it could be observed that the value of equity shares is computed by discounting the future dividend with the discount rate which is cost of equity in this case. The current dividend (D0) is multiplied by the growth rate to compute the future dividend and discounting is applied on this figure to get the value of share as on today.
Further, the value of bond is also computed with reference to the discounted value of the interest payment and the discounted value of the maturity value (Shim and Siegel, 2008). The formula used to determine the value of bond is as under:
Here, “C” refers to coupon payment, “I” is the discount rate, “m” is maturity value, and “n” is the number of periods.
The concept of time value of money entails that the value of dollar today would not be equal to the value of dollar tomorrow. Thus, applying this concept, the value of bond is computed. The value of bond is equal to the sum of present value of all coupon pavements to be made over the terms of maturity and present value of maturity value (Shim and Siegel, 2008).
The value of preference shares is also computed applying the concept of time value of money. The value of preference share is arrived at by discounting the dividends to be received in future and amount which would be received at the time of redemption.
Apart from the use in valuation of security, the concept of time value of money is also used in capital budgeting decisions. Capital budgeting refers to the process of analyzing the financial viability of long term investments (Shapiro, 2008). There are various techniques such as net present value, payback period, internal rate of return, and profitability index which are applied in capital budgeting decisions. The net present value technique is based on the concept of time value of money. In this technique, the present value of cash inflows is computed with the application of discount rate. The value of initial investment is deducted from the total present value of cash inflows and result is known as net present value (Shapiro, 2008).
The discount rate is determined with reference to different parameters in different situations. In one case, the discount rate may be determined with reference to the borrowing rate and another it may be determined with reference to the cost of equity. Further, the discount rate is adjusted for the risk premium and inflation effect. The higher the risk higher will be the discount rate and higher the discount rate lower will be the present value. The discounting of cash flows is done only after adjusting the discount rate with the risk premium and inflation (Shapiro, 2008).
Therefore, it may be concluded from the overall discussion that the concept of time value of money forms the basic premise of the financial management. The crucial financial management decisions involving capital budgeting and investment decisions are based on the concept of time value of money. The application of time value of money concept is wide spread from valuation of securities to the investment in plant and machinery.
Studebaker is concerned about accumulating funds for his retirement. At present he is 30 years of age and he wants to accumulate funds till his retirement at the age of 60 years. Studebaker presently has investment in the money market mutual funds. He sought advice from the finance specialist to take out a single life insurance policy for 20 years to accumulate funds for his retirement. Thus, the goal of Studebaker is to accumulate money for his retirement which appears to be correct. At his retirement, the income from salary would discontinue and he would require some source of income at that moment to finance his spending.
|
Investment made |
550000 |
|
|
Interest rate per annum |
6% |
|
|
Period (years) |
20 |
|
|
Accumulated amount |
$1,763,924.51 |
The amount invested is $550,000 at the rate return of 6% per annum. Applying the compounding technique, the value accumulated in the investment after 20 years would be 1763,925. For the purpose of compounding following equation has been used:
FV=PV*(1+r)^n
The computation of yearly payments on the mortgage loan has been computed as below:
|
30 years |
20 years |
|
|
Loan amount |
705000 |
705000 |
|
Interest rate per annum |
9% |
9% |
|
Period (years) |
30 |
20 |
|
Yearly payment |
$68,622.13 |
$77,230.26 |
It could be observed that the yearly payment for mortgage of $705,000 with interest rate of 9% and time period of 30 years is $68,622.13. The yearly payment changes to $77230.26 if the period is reduced to 20 years. The yearly payments have been computed applying the following formula:
The loan balance at the end of 19th and 20th year on the mortgage of $705,000 with interest rate 9% and time of 30 years is given below:
|
Year |
Opening balance |
Installment |
Interest |
Closing balance |
|
19 |
$491,384.20 |
$68,622.13 |
44224.6 |
$466,986.66 |
|
20 |
$466,986.66 |
$68,622.13 |
42028.8 |
$440,393.33 |
(Appendix-1)
The closing balance of 19th year has been computed by reducing the closing balance of 18th year by the principal repaid in the 19th year. The computations for 20th year have also been done in the similar way.
Yes, it is true that $550,000 invested in the single life insurance policy would increase accumulate to $1,763,925 in 20 years time at interest rate of 6% per annum. However, the amount for investment in the life insurance would be arranged from the new mortgage of $250,000 so the debt of Studebaker would increase by $250,000. The increase in debt would also increase the yearly repayments from $42,476.82 to $68,622.13.
The accumulated amount over the period of 20 years would be $1,398,287.14 as computed below:
FV=PV*(1+r)^n
|
Investment made |
300000 |
|
Interest rate per annum |
8% |
|
Period (years) |
20 |
|
Accumulated amount |
$1,398,287.14 |
The amount accumulated after 20 years on investment of 26145.31 each year at interest rate of 8% would be as under:
|
Investment made each year |
26145.31 |
|
Interest rate per annum |
8% |
|
Period (years) |
20 |
|
Accumulated amount |
$1,196,460.74 |
The amount accumulated in 20 years time on an investment of $550,000 with a rate of interest of 7% per annum would be as under:
FV=PV*(1+r)^n
|
Investment made |
550000 |
|
Interest rate per annum |
7% |
|
Period (years) |
20 |
|
Accumulated amount |
$2,128,326.45 |
As per the evaluation done by Comer, the single premium life insurance policy is an unattractive investment. The criticism of single life insurance policy done by Comer is correct. Studebaker could earn more by investing $300,000 and a further sum of $26,145.31 each year at the interest rate of 7%. The total amount accumulated under the single life insurance policy would be $1,763,925 which is lower than the accumulated sum of $2,594,748 ($1,398,287+$1,196,461).
Studebaker will have to save $214,064.10 each year to accumulate $3,500,000 in 20 years time. The computations are shown below:
|
Future value |
(3,500,000.00) |
|
Time period |
20 |
|
Rate |
8% |
|
Investment made |
300,000.00 |
|
Value of Investment at end of 20 years |
$1,398,287.14 |
|
Amount required to be recovered (3500000-1398287.14) |
(2,101,712.86) |
|
Amount yearly (using pmt function) |
$214,064.10 |
In this case, Studebaker will have to save $279,538.37 each year to accumulate $3,500,000 in 20 years time. The computations are shown below:
|
Future value |
(3,500,000.00) |
|
Time period |
12 |
|
Rate |
8% |
|
Investment made |
300,000.00 |
|
Value of Investment at end of 12 years |
$755,451.04 |
|
Amount required to be recovered (A-E) |
(2,744,548.96) |
|
Time period |
20 |
|
Rate |
8% |
|
Amount yearly (using pmt function) |
$279,538.37 |
|
Loan amount |
(705,000.00) |
|
Time period |
20 |
|
Rate |
8% |
|
Yearly repayment |
68,622.00 |
|
12th of yearly payment |
5,718.50 |
Monthly EMI: P*R*(1+r)^n/(1+r)^n-1
|
Loan amount |
(705,000.00) |
|
Time period (months) |
240 |
|
Rate (monthly) |
0.67% |
|
EMI (monthly) |
$5,896.90 |
Thus, it could be observed that the 12th of annual repayments is not equal to monthly repayment. The monthly repayment is $5,896.90 and 12th of annual repayment is $5,718.50.
The value of cost of investment of insurance in the 20th year has been computed by applying the future value formula:
FV=PV*(1+r)^n
|
Yearly cost of insurance on 1st year |
47145.31 |
|
Interest rate per annum |
7% |
|
Period (years) |
19 |
|
Yearly cost of insurance on 20th year |
$170,502.31 |
Morton suggested Studebaker making investment in a single life insurance policy to accumulate the funds for retirement. For this purpose, he suggested to take out a mortgage of $250,000 and invest the amount along with a sum of $300,000 held in the mutual funds. Thus, he suggested taking out a life insurance policy for $550,000 which would accumulate a sum of $1,763,925 over the period of 20 years. However, the strategy suggested by Morton is not financial beneficial for Studebaker. The cost of mortgage at 9% would increase the expenses more than the income accrued on the life insurance policy.
The proposed investment plan involves taking out a mortgage for $250,000 and investing in a single life insurance policy for a sum of $550,000, a sum of $300,000 of which could be arranged by liquidating the investment in mutual funds. The investment plan shown by Morton indicates that it would be beneficial for Studebaker to take out the life insurance policy. But the actually it ignores the opportunity cost, certain out of pocket expenses, and taxes. When the opportunity cost, out of pocket expenses, and taxes are considered, the investment in life insurance policy would not be beneficial. It is clear from the answer to question-6 above that Studebaker can accumulate a sum of $2,594,748 by simply investing the money available at 8% interest. The accumulated amount on the life insurance policy would be $1,763,925 which is less than what Studebaker could accumulate otherwise. Hence, the proposed investment plan is not financial beneficial to Studebaker.
References
Baker, H.K. and English, P. 2011. Capital Budgeting Valuation: Financial Analysis for Today’s Investment Projects. John Wiley & Sons.
Drake, P.P. and Fabozzi, F.J. 2009. Foundations and Applications of the Time Value of Money. John Wiley & Sons.
Halpin, D.W. and Senior, B.A. 2011. Financial Management and Accounting Fundamentals for Construction. John Wiley & Sons.
Shapiro. 2008. Capital Budgeting And Investment Analysis. Pearson Education India.
Shim, J.K. and Siegel, J.G. 2008. Financial Management. Barron’s Educational Series.
Silver, T.L. 2011. The Time Value of Life: Why Time Is More Valuable Than Money. iUniverse.
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