Then, considering that project A and B both cost $100 today however, with project A expected to generate higher amount of $200 tomorrow compared to merely $100 expected to be generated by project B Larry would invest in project A. The reason for such decision is that the project A is expected generate $100 higher in return tomorrow compared to project B at same level of investment (Sofat & Hiro, 2015).
Still the preference of the investor would not change as the motive behind investment of an investor would be to optimize the amount return on his or her investment thus, with the above utility function Marry’s choice of investment would be project A as well as it expects to generate $200 tomorrow compared to $100 that is expected to be generated by project B.
Hence, Marry would also invest in project A.
Marry would invest in project A to generate higher return in the future.
Marry would borrow (1000 – 700) = $300 at net interest rate of 10%.
To get optimal investment,
Optimal consumption would be Co = 43.57 and C1 = 58.23.
If Bob has following utility function:
Then, he will invest as per the following assumption:
Using the Canadian Mortgage Convention the monthly mortgage payment for the mortgage loan of $800,000 from Bank of Montreal to buy house and a fixed rate of 6% a year with 5 year closed is $5,929.71 per month (Bryce, 2017).
For the 24th monthly payment out of the monthly mortgage payment of $5,929.71 principal amount is $1,886.54 and $3,810.97 is for interests.
Instead of monthly payment if the borrower changes the schedule of payment to weekly then the weekly mortgage payment would be $1,362.24.
|
Payment sequence |
Payments ($) |
PV factors |
|
|
1 |
50 |
0.6139133 |
30.6956627 |
|
2 |
50 |
0.5338376 |
26.6918806 |
|
3 |
50 |
0.4642066 |
23.2103309 |
|
4 |
50 |
0.4036579 |
20.1828965 |
|
5 |
50 |
0.3510069 |
17.5503448 |
|
6 |
50 |
0.3052234 |
15.2611694 |
|
7 |
50 |
0.2654116 |
13.2705821 |
|
8 |
50 |
0.2307927 |
11.5396366 |
|
9 |
50 |
0.2006893 |
10.0344666 |
|
10 |
50 |
0.1745125 |
8.7256231 |
|
11 |
50 |
0.1517500 |
7.5874984 |
|
12 |
50 |
0.1319565 |
6.5978247 |
|
13 |
50 |
0.1147448 |
5.7372388 |
|
14 |
50 |
0.0997781 |
4.9889033 |
|
15 |
50 |
0.0867635 |
4.3381768 |
|
16 |
50 |
0.0754466 |
3.7723277 |
|
17 |
50 |
0.0656057 |
3.2802849 |
|
18 |
50 |
0.0570484 |
2.8524217 |
|
19 |
50 |
0.0496073 |
2.4803667 |
|
20 |
50 |
0.0431368 |
2.1568406 |
|
21 |
50 |
0.0375103 |
1.8755136 |
|
22 |
50 |
0.0326176 |
1.6308813 |
|
23 |
50 |
0.0283632 |
1.4181577 |
|
24 |
50 |
0.0246636 |
1.2331806 |
|
25 |
50 |
0.0214466 |
1.0723310 |
|
26 |
50 |
0.0186492 |
0.9324617 |
|
27 |
50 |
0.0162167 |
0.8108363 |
|
28 |
50 |
0.0141015 |
0.7050750 |
|
29 |
50 |
0.0122622 |
0.6131087 |
|
30 |
50 |
0.0106628 |
0.5331380 |
|
31 |
50 |
0.0092720 |
0.4635983 |
|
32 |
50 |
0.0080626 |
0.4031289 |
|
33 |
50 |
0.0070109 |
0.3505469 |
|
34 |
50 |
0.0060965 |
0.3048234 |
|
35 |
50 |
0.0053013 |
0.2650638 |
|
36 |
50 |
0.0046098 |
0.2304903 |
|
37 |
50 |
0.0040085 |
0.2004263 |
|
38 |
50 |
0.0034857 |
0.1742838 |
|
39 |
50 |
0.0030310 |
0.1515511 |
|
40 |
50 |
0.0026357 |
0.1317836 |
|
41 |
50 |
0.0022919 |
0.1145944 |
|
42 |
50 |
0.0019929 |
0.0996473 |
|
43 |
50 |
0.0017330 |
0.0866498 |
|
44 |
50 |
0.0015070 |
0.0753477 |
|
45 |
50 |
0.0013104 |
0.0655197 |
|
46 |
50 |
0.0011395 |
0.0569737 |
|
47 |
50 |
0.0009908 |
0.0495423 |
|
48 |
50 |
0.0008616 |
0.0430803 |
|
49 |
50 |
0.0007492 |
0.0374611 |
|
50 |
50 |
0.0006515 |
0.0325749 |
|
51 |
50 |
0.0005665 |
0.0283260 |
|
52 |
50 |
0.0004926 |
0.0246313 |
|
53 |
50 |
0.0004284 |
0.0214185 |
|
54 |
50 |
0.0003725 |
0.0186248 |
|
55 |
50 |
0.0003239 |
0.0161955 |
|
56 |
50 |
0.0002817 |
0.0140830 |
|
57 |
50 |
0.0002449 |
0.0122461 |
|
58 |
50 |
0.0002130 |
0.0106488 |
|
59 |
50 |
0.0001852 |
0.0092598 |
|
60 |
50 |
0.0001610 |
0.0080520 |
|
61 |
50 |
0.0001400 |
0.0070017 |
|
62 |
50 |
0.0001218 |
0.0060885 |
|
63 |
50 |
0.0001059 |
0.0052943 |
|
64 |
50 |
0.0000921 |
0.0046038 |
|
65 |
50 |
0.0000801 |
0.0040033 |
|
66 |
50 |
0.0000696 |
0.0034811 |
|
67 |
50 |
0.0000605 |
0.0030270 |
|
68 |
50 |
0.0000526 |
0.0026322 |
|
69 |
50 |
0.0000458 |
0.0022889 |
|
70 |
50 |
0.0000398 |
0.0019903 |
|
71 |
50 |
0.0000346 |
0.0017307 |
|
72 |
50 |
0.0000301 |
0.0015050 |
|
73 |
50 |
0.0000262 |
0.0013087 |
|
74 |
50 |
0.0000228 |
0.0011380 |
|
75 |
50 |
0.0000198 |
0.0009895 |
|
76 |
50 |
0.0000172 |
0.0008605 |
|
77 |
50 |
0.0000150 |
0.0007482 |
|
78 |
50 |
0.0000130 |
0.0006506 |
|
79 |
50 |
0.0000113 |
0.0005658 |
|
80 |
50 |
0.0000098 |
0.0004920 |
|
81 |
50 |
0.0000086 |
0.0004278 |
|
82 |
50 |
0.0000074 |
0.0003720 |
|
83 |
50 |
0.0000065 |
0.0003235 |
|
84 |
50 |
0.0000056 |
0.0002813 |
|
85 |
50 |
0.0000049 |
0.0002446 |
|
86 |
50 |
0.0000043 |
0.0002127 |
|
87 |
50 |
0.0000037 |
0.0001850 |
|
88 |
50 |
0.0000032 |
0.0001608 |
|
89 |
50 |
0.0000028 |
0.0001399 |
|
90 |
50 |
0.0000024 |
0.0001216 |
|
91 |
50 |
0.0000021 |
0.0001057 |
|
92 |
50 |
0.0000018 |
0.0000920 |
|
93 |
50 |
0.0000016 |
0.0000800 |
|
94 |
50 |
0.0000014 |
0.0000695 |
|
95 |
50 |
0.0000012 |
0.0000605 |
|
96 |
50 |
0.0000011 |
0.0000526 |
|
97 |
50 |
0.0000009 |
0.0000457 |
|
98 |
50 |
0.0000008 |
0.0000398 |
|
99 |
50 |
0.0000007 |
0.0000346 |
|
100 |
50 |
0.0000006 |
0.0000301 |
|
Present value of the cash flows |
235.33 |
Thus, present value of these cash flows is $235.35.
Bond 1 yield (%) = (1000 -975) x 100 / 975 = 2.56410%
|
Yield (%) |
|
|
Bond 1 |
2.564103 |
Approximately 2.56%
Bond 2 coupon rate is 8%
|
Bond 2 |
||
|
Price |
1018.86 |
|
|
Yield (1018.86 x 4% c 2) |
81.5088 |
40.7544 |
|
Coupon rate |
8 |
Bond 3 price would be equal to its face value, i.e. $1,000 because the yield and coupon rate of the bond are equal. Hence, the price of the bond would be $1,000, i.e. exactly the face value of the bond.
The term structure of spot rates for 1 year to 3 years maturity is higher spot rate with increase in maturity period as per the information of the bond here.
|
Particulars |
Amount ($) |
|
Price of the bond |
1,040.00 |
|
Face value |
1,000.00 |
|
Annual interest @6% |
60.00 |
|
Maturity period |
2 years |
|
Total amount of interest earned (60 x 2) |
120.00 |
|
Face value at the time redemption |
1,000.00 |
|
Total cash inflow |
1,120.00 |
|
Less: Cash outflow at the time of investment |
1,040.00 |
|
Profit over 2 years |
80.00 |
|
Particulars |
Amount ($) |
|
Investment |
1,000.00 |
|
Add: Interest (1000 x 4%) |
40.00 |
|
Total investment |
1,040.00 |
|
Face value |
1,000.00 |
|
Coupon (1000 x 5%) |
50.00 |
|
Total inflow |
1,050.00 |
|
Return (1050 -1040) |
10.00 |
Hence, holding period return is $10 for Bond 3.
True, in case no opportunity of arbitrage the zero coupon bond rate would never trade at premium as without any interest there would be no possibility of earning any return on zero coupon bond without the arbitrage opportunity. Hence, zero coupon bond without arbitrage opportunity would never trade at a premium.
Term structure of sport rates for 1 year to 4 year maturity is calculated in the table below:
|
Forward rates |
|
|
f1 |
2% |
|
f2 |
2.5% |
|
f3 |
3% |
|
f4 |
4% |
|
Term structure |
2.875%Market rate of interest 6% has been assumed. |
|
Year |
Coupon + face value |
PV factor @6% pa. |
Present value ($) |
|
1.00 |
80.00 |
0.9434 |
75.47 |
|
2.00 |
80.00 |
0.8900 |
71.20 |
|
3.00 |
1,080.00 |
0.8396 |
906.79 |
|
Price of the bond |
|
1,053.46 |
No arbitrage annualized forward rate that can be locked in today for the loan is 9,325.00
Market value of forward loan with r1 = 3% is $9,716.98
|
Year |
Market interest rate 6% pa. |
Spot rate @3% |
|
|
1 |
0.9433962 |
0.970874 |
$9716.981 |
Market value of forward loan with r2 = 3.5% is $9,764.15.
|
Year |
Market interest rate 6% pa. |
Spot rate @3.5% |
|
|
1 |
0.9433962 |
0.966184 |
9764.151 |
Market value of forward loan with r2 = 3.75% is $9,787.74.
|
Year |
Market interest rate 6% pa. |
Spot rate @3.75% |
|
|
1 |
0.9433962 |
0.963855 |
9787.736 |
|
EPS year 0 |
20 |
|
EPS year 1 |
25 |
|
EPS year 2 |
30 |
|
EPS year 3 |
34.5 |
|
EPS year 4 |
37.95 |
|
Dividend in year 4 |
18.975 |
|
Indefinite growth rate |
10% |
|
Discount rate |
15% |
|
Share price (18.975 / 15% -10%) |
$379.5 |
Thus, estimated share price is $379.50.
The stock price in such case would be,
|
EPS year 0 |
20 |
|
Share price (10 / 15% -10%) |
$200 |
The steady-state earnings growth rate of Cindy is 18%.
References:
Bryce, H. J. (2017). Financial and strategic management for nonprofit organizations. Walter de Gruyter GmbH & Co KG.
Sofat, R., & Hiro, P. (2015). Strategic financial management. PHI Learning Pvt. Ltd..
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