Income Per Capita, Annual Inflation, Investment, And Time Value Of Money

The Reason for taking 1$ today rather than at some point of time

Questions:

Question 1: Concept of Time Value of Money

By using the concept of time value of money, please use a few sentences plus numerical example to show your understanding in the following questions:

a. Why is it better to receive $1 today than at some point in the future?

b. During the global financial crisis, interest rate in Australia fell to low levels, but some relatively safe investments such as bank deposits were just barely above zero in United States. If the interest rate is actually zero, what is the relationship between the present value and the future value of money?

c. What is the importance to an individual and corporate manager of understanding time value of money concepts? Under what circumstance would the time value of money be irrelevant from the perspective of corporate view?

Question 2: Present Value and Future Value

As a winning team of Dragon Boat Race Competition in WA, your team was given to choose one of the following prizes:

a. $100,000 now.

b. $180,000 at the end of five years.

c. $11,400 a year forever.

d. $19,000 for each of 10 years.

e. $6,500 next year and increasing thereafter by 5 per cent a year forever.

Your team was dazzled by these options, and the other team members turned to you for your help as you are studying finance courses in a university. If the interest rate is 12 per cent, how are you going to help your team to make the choice? (Please state detailed calculations, reasons, and the logic leading to your choice).

Question 3: Present Value, Future Value, and Inflation Rate

The following table shows national income per capital in 2013 in a sample of OECD countries and recent rates of inflation:

	Income per capital	Annual inflation
	(US$)	(%/year)
Australia	65,520	2.7
France	42,250	0.69
Germany	46,100	1.43
Greece	22,530	-1.71
Japan	46,140	1.61
Switzerland	86,600	0.07
Turkey	10,950	7.4
UK	39,140	1.2
USA	53,670	1.5

If recent inflation rates persist in the future, what nominal income will be needed in each country in 2020 just to keep pace with inflation?

Question 4: Effective Interest Rate

You and your partner want to buy a house.

City Bank will give you a $200,000 loan for 20 years. They will charge you 5% concessional interest for the first year, after which the loan reverts to their normal variable rate, which is currently 8.75%. They will also charge you a $600 application fee, plus when you make your loan enquiry you can have as much coffee as you can drink.

The Republic Bank will also give you a $200,000 loan for 20 years, but their concessional interest rate for the first year is 6.75%, after which the loan reverts to their normal variable rate, which is also 8.75%. However, there is no fee and no coffee.

Both banks compound interest daily and you will make your loan payments fortnightly. Assume there are 26 fortnights per year (520 over 20 years), and banks use a 365-day year to calculate the interest charge.

Required:

a. What would your fortnightly loan payment be for each bank?

b. Assuming you can drink $5 worth of coffee, which bank offers the best deal.

Question 5: Present Value and the Opportunity Cost of Capital

Kwinana Explorations Ltd have just struck oil in Western Australia. Their share price jumps from $1 to $15.

Required:

a. Explain why the equilibrium price has changed.

b. Do you think the required rate of return for Kwinana will have changed?

c. Assume the required rate of return does not change and is 20 per cent. Assume investors had believed there was no chance of an oil strike and expected that the company would wind up at the end of the year. How large a liquidating dividend had they expected? If the company is now to be sold to a multinational oil company at the end of the year, how much do investors expect to get per share?

d. Using your answers from Part ©, calculate the expected return before and after news of the oil strike.  

e. Assume you got early news of the oil strike. What should you do, and what would be your expected return?

f. Calculate the NPV of investing $1000 in Kwinana immediately before the news of the oil strike, and calculate NPV of a $1000 investment made immediately after the news.

Question 6: Bond

Imagine it is year 1815 and you are a trader in British government consols (consolidated war loan – a perpetual security). It is the morning of Monday 19 June, the day after the battle of Waterloo. The British were the victors, but the battle was not decided until about nine in the evening. You believe that currently you are the only trader who knows the outcome of the battle.

Would you be buying or selling consols? Explain your answer.

Question 7: Share Valuation

Investors expect the following series of dividends from a particular ordinary share: Year 1 $1.10

Year 2 $1.25
Year 3 $1.45
Year 4 $1.60
Year 5 $1.75

After the fifth year, dividends will grow at a constant rate. If the required rate of return on this equity is 9% and the current market price is $45.64.

Required:

a. What is the long-term rate of dividend growth expected by the market?

b. In the dividend constant-growth model we can apply the equation that P=D/(r-g) only under the assumption that r>g. Suppose someone tries to argue with you that for a certain share, r < g forever, not just during a temporary growth spurt. Why can’t this be the case? What would happen to the share price if this were true? If you try to answer simply by looking at the formula you will almost certainly get the wrong answer. Think it through.

Question 8: Investment Decision

As a chief financial officer of Delta Pharmaceuticals, you recently received a capital expenditure analysis from your financial team. The two selection criteria results are presented below:

Global financial catastrophe during 2008

	Investment	NPV	IRR
Project	($,000)	($,000)	(%)
1	300	66	17.2
2	200	-4	10.7
3	250	43	16.6
4	100	14	12.1
5	100	7	11.8
6	350	63	18
7	400	48	13.5

Your company has only $1 million allocated for capital expenditures. The cost of capital for each project is 11 per cent.

Required

a. Which of the above projects should the company accept to stay within the $1 million budget?

b. How much does the budget limit cost the company in terms of its market value?

a. The Reason for taking 1$ today rather than at some point of time because the  dollar received today can be invested  to make more money in future. Apart from that, saving today allows to earn interest on their saving  of 1$ which will give higher return in future (Andriosopoulos and Lasfer 2014).

b. Global financial catastrophe during 2008 has created housing bubble and lowered the bam interest rate which affected the future value of present invested money. Since the interest is zero then the present value of money would be decreases which would decrease the future value of money. Interest rate for the money is zero would decreases the PV which would again decreases the FV.

The relationship between PV and FV is if one increases, the other increases assuming that the interest rate and number of periods remains constant.

c. One of the major concepts of time value of money is that money received at different period of time has different value. The corporate manager sees the time value of money ahs opportunity for increasing its funds in future. The fundamental behvaiour behind the this thought is that money the company receive in future would  have less purchasing power  that money the company own now , this is because of the rising inflation rate (Connor  2006).  As for the individuals, if the individuals need $50000 after the retirement from the job of 10 years. The amount needed to deposit at every year from now would be determine the by using the time value of money.

The time value of money affects corporate managers when budgeting and planning for fiscal years will be helping the company to manage and control the expenditure.

The time value of money will be irrelevant if the interest rate is not given.  Future value is irrelevant if the future value is double the present value of investment. Apart from the above, if the time of the future is value of the investment not been given then it will be  irrelevant (McSweeney  2006).

 Time= Money/Cost 

As wining prizes , the team will be choosing the $100,000 now because as per the time value of money the money which will be received today will give higher return in future rather than future money.

100,000 *12%= 12000 per month from now onwards

Which means , the team will be able to receive= 144000 total at end of every year

This shows = 144000 x 5 years = 720,000 in future.

This will be higher than the 180000 at the end of five years where the team will only be able to receive 3000 per month till five years.

The major concepts of time value of money

From the above, it has been found that money which will be received today will give higher value because the purchasing power of the money is decreasing every year (McSweeney  2006). Besides that, the time value of money   will give an insight of the earnings from the present value of money per month.

FVOA= A* (1+r)ⁿ-1/r

=100,000 x (1+0.12)⁵-1/5

=100000 x 0.15

= 15246.83

The rest of the option like 180000 for five year ending , 114000  year forever , 19000 for each years of 10 years and 6500 for forever only decrease the value of money future because as the inflation rate is been increasing  and the value of money will be decreasing future. 

	Income per capita	Annual inflation rate %	Nominal income  (2013- 2020)
Australia	65520	2.7	5326.534874
France	42250	0.69	3028.52
Germany	46100	1.43	3388.065
Greece	22,530	-1.71	-22259.92
Japan	46140	1.61	49251.74
Switzerland	86,600	0.07	8734.394
Turkey	10,950	7.4	1233.33
UK	39140	1.2	2877.94
USA	53,670	1.5	4036.92

FVOA = A x (1+r)ⁿ -1/r

Australia	France	Germany	Greece
1.0495	0.0079	0.0162	0.0219
1.402	1.0079	1.0162	-1.164
0.402	1.056628003	1.11906	-2.164
0.08129632	0.056628003		-0.988
5326.534874	0.071681017	0.11906	-22259.92382
	3028.52	0.0735
		3388.065432
Japan	Switzerland	Turkey	UK	USA
0.0401	0.1199	2.75	1.125	1.173
1.0401	1.1199	1.75	0.0735	0.075
1.317	2.209	0.113	2877.94	4036.92
1.067	1.209	1233.33
49251.74	0.101
	8734.394

a.

City Bank

Loan = 200000

Interest for 1^st year = 5%

Fortnight = 14 days

Compound interest daily

EAR = 1+(i/m)^m – 1

EAR = 1+(0.05/14)¹⁴ –  1

EAR = 5.118%

F.V. = 3,951,907.97

Application fee = 600

F.V. = 3,951,907.97 + 600 = 3,952,508

Loan = 200000

Interest for 1^st year = 6.75%

Fortnight = 14 days

Compound interest daily

EAR = 1+(i/m)^m – 1

EAR = 1+(.0675/14)¹⁴ – 1

EAR = 6.966%

F.V. = 4,499,141

Both of the bank have  to pay 3,952,508 and 4499,141 of fortnightly loan payment.  This shows that bank will have to pay more than what it was expected.

b.If I drink 5$ worth of coffee then the bank of then I will be choosing the republic banks.  One of the major reason for choosing the bank because it charges less interest  on  coffee and offers a best deal  for the client and the company.

a. The the equilibrium price of the market has been changed because of the Kwinana has purchased the oil field in Western Australia.

b. The required of rate of return of the company will be changed because the share price of the company has been jump off from $1 to $15. Since the price of the company has changed it made the company to gain the large or pool of investor who are willing to invest in the company.

c. If the company rate of return is not been changed and company is looking to winding up the then investors will get the small percentage of the investment as dividend because of the company has to settle its debt and preference shares.

Apart from that, if the Kwinana is looking to sell its company to the largest MNC then they expect share of return will be given as per the share purchased by the investors (Svennebring et al.  2013).

d. Expected rate of return would be before news of oil strike would be higher with $15 and after the news the shareholding of the demand will decreased upto $1.20. This shows that strike and other external threats make the investors to change decisions on investment.

As per the situation I will sell the shares of the British government consoles. I would sell the loan to as because I know the fate of the war already. The buying of loan would make would cost me higher because of the government has not yet announced when it will be repaying the debt.  The money which I will receive today will be more valuable than the tomorrow money. It is simply time value calculations. After the battle is won the government will take at least more than 8-10 years to repay the consolidated loan.

a.

Present Value (P)	45.64
Return on Equity (Ke)	9%
Expected Dividend (D1)	1.75

The long term growth rate of dividend shows that , expected dividend is 1.75. These investors who are investing more than 1.45 is very much helpful to gain the long term benefits in future.   

b.

P = D1/(Ke – g)

45.64 =  1.75/(0.09 – g)

g = 0.052%

With the help of dividend constants growth model shows the growth of shares by 0.052%. This is because of the assumption under r>g.  If the scenario is just opposite with r

Project	Investment	NPV
1	300	66
2	350	63
3	400	48
4	250	43
5	100	14

Project	Investment	IRR (%)
1	350	18
2	300	17.2
3	250	16.6
4	400	13.5

a. If the company has one million budget then the company will be choosing highest NPV value giving project such 66, 63 and 43 are the annual return.  As per the IRR , the chosen investment rate here would be 18, 17.2 and 16.6.

 From the above calculation the chosen portfolio investment project for the delta pharmaceuticals would be 350, 250 and 300=900. The rest would be left out.

b. As per the budget limit has cost the company to choose only those project which has higher NPV such as 66, 63 , 14 and 43 . however, although the 48 has highest rate of return but it fails to fulfill the 1 million project therefore the 14 npv has been chosen which is has investment worth of $100.

Reference List

Andriosopoulos, Dimitris, and Meziane Lasfer. 2014. ‘The Market Valuation Of Share Repurchases In Europe’. Journal Of Banking & Finance. doi:10.1016/j.jbankfin.2014.04.017.

Connor, Tom. 2006. ‘Net Present Value: Blame The Workman Not The Tool’. Strat. Change 15 (4): 197-204. doi:10.1002/jsc.766.

McSweeney, Brendan. 2006. ‘Net Present Value: The Illusion Of Certainty’. Strat. Change 15 (1): 47-51. doi:10.1002/jsc.746.

Svennebring, Andreas M, and Jarl ES Wikberg. 2013. ‘Net Present Value Approaches For Drug Discovery’. Springerplus 2 (1): 140. doi:10.1186/2193-1801-2-140.