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Investment Banks and Financial Institutions
ORDER INSTRUCTIONS:
Investment Banks and Financial Institutions
1. Answer questions 4-8 in the attached document.
2. Answer Problems 35, 37, 39, and 41 in the attached documents then answer them again using the below scenarios.
3. Redo problem 35, assuming a coupon rate of 8% in part a, and yields to maturity of 12 and 12.5% in part b ?
4. Repeat problem 37, assuming that the zero coupon bond has 7 years to maturity.
5. Repeat problem 39, assuming that the three bonds under consideration have 6 years to maturity.
6. Repeat problem 41, assuming that the fair present value rose from $975 to $ 990.
Investment banking is the division of a bank or financial institution that serves governments, corporations, and institutions by providing underwriting (capital raising) and mergers and acquisitions (M&A) advisory services. Investment banks act as intermediaries between investors (who have money to invest) and corporations (who require capital to grow and run their businesses).
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Investment Banks and Financial Institutions
PART 1
Questions 4 to 8
Question 4
Identify whether a bond will be considered a premium bond, a discount or a par bond
a) A bond with a market price higher than its par value is a premium bond
b) A bond with a coupon rate equals to its yield to maturity is considered a par bond
c) A bond with a coupon rate less than the required rate of return is considered a discount bond
d) A bond whose coupon rate is less than its yield to maturity is considered a discount bond
e) A bond whose coupon rate is greater than its yield to maturity is considered a premium bond
f) a bond whose fair value is less than its face value is considered a discount bond
Question 5
How equity valuation differ from bond valuation
Valuation of equity onsiders dividend on stock, growth rate, rate of return. These considerations are appropriate where an entity uses dividend growth model
formular where dividend growth factor is equal throughout: Po = D1/r – g
where dividend growth factor is not equal: Po = {Dn (1 + gn)/r – g} (1/(1 + r)n)
Valuation of bond considers bond coupon rate, investors required rate of return, maturity value and maturity period
Formulae = (Intr x PVAF) + (MV x PVIFrn)
Question 6
What happens to the fair present value of a bond when the required rate of return on the bond increases
An increase in required rate of return lowers the fair present value of a bond
Question 7
A change in interest rate affects the price of of both short and long because change in interest rate affects the yield of both and long and short-term loan
Long-term bond’s price is more affected by increase in interest rate due to long duration they cove
Question 8
Bond’s price with large coupon rate are affected with the change in interest rates more than bond’s price with a small interest rate.
This is because large coupon rate reduces bond’s price by a larger margin.
Investment Banks and Financial Institutions
PART 2
Aswer problems
Problem 35
a) what is the duration of a five year treasury bond with a 10% semi-annual selling at per
periods = 2 x 5 years = 10 periods
par value= $1000
coupon = 10%/2 = 5%
interest = 5% x 1000 = 50
bond = (50 x PVIF 10 periods @ 5%) + (1050 x PVIF10 periods @5%) =
= 47.62 + 952.38 X10 = $9571.42
Price = 952.38 + 47.62 = $1000
period = 9571.42/1000 = 9.57/2 = 4.78
b) duration if the yield to maturity increases to 14% and 16%
1st period interest 14% x 1000 x 1/1+0.14 = 122.81
2nd (140 + 1000 ) x 0.7695 = 877.19
(877.19 x 10 ) + 122.81 = $8894.71
price = 1000
8894.71/1000 = 8.89/2 = 4.4 YEARS
At 16%
1st period interest 16% x 1000 x 1/1+0.16 = 137.93
2nd (160 + 1000 ) x 0.7432 = 862.07
(862.07 x 10 ) + 137.93 = $8758
price = 1000
8758.62/1000 = 8.75/2 = 4.3 years
c) Conclusion
An increase in bond yield to maturity reduces the duration of a bond. This is because an increased yield to maturity increases the cash inflow hence reducing the period of maturity
Problem 37
Duration of zero coupon bond that has eight years to maturity
The duration of a bond with a zero coupon rate is the same its maturity date. Thus the duration of the bond is 8 years
if the duration of maturity increases to 10 years, bo nd duration will be 10 years
if the maturity increases to 12 years, bond duration will be 12 years
Problem 39
a) At 8%
interest = 8% x 10000 = 800
1st 800 x 0.9259 = $740.74
2nd (800 + 10000) x 0.8573 = 9259.26
total = (9259.26 x 5) + 740.74 = $47036.29/10000 = 4.7 years
b) at 10%
interest = 10% x 10000 = 1000
1st 1000 x 0.9091 = $909.10
2nd (1000 + 10000) x 0.8264 = 9090.91
Total = (9090.91 x 5) + 909.1 = $46363.65/10000 = 4.6 years
c) coupon rate 12%
interest = 12% x 10000 = 1200
1st 1200 x 0.8929 = $1071
2nd (1071 + 10000) x 0.7972 = 8825.73
Total = (8825.73 x 5) + 1071= $45199.67/10000 = 4.5 years
Problem 41
At 9.75%
interest = 9.75% x 975 = $95.06
at 9.25%
interest = 9.25% x 995 = $92.04
995/92.04 = 974/95.06 = 10 years
Investment Banks and Financial Institutions
PART 3
Problem 35
a) Coupon rate of 8%
interest = 8% x 1000 = 80
1st 80 x 0.9259 = $74.07
2nd (80 + 1000) x 0.8573 = 925.92
total = (925.92 x 5) + 74.07 = $4703.63/10000 = 4.7 years
b) yield to maturity is 12%
interest = 12% x 1000 = 120
1st 120 x 0.8929 = $107.1
2nd (107.1 + 1000) x 0.7972 = 882.57
Total = (882.57 x 5) + 107.1= $4519.96/1000 = 4.5 years
Yield to maturity is 12.5%
interest = 12.5% x 1000 = 125
1st 125 x 0.8889 = $111.1
2nd (111.1 + 1000) x 0.7901 = 877.91
Total = ( 877.91 x 5) + 111.1= $4500.63/1000 = 4.5 years
Investment Banks and Financial Institutions
PART 4
Problem 37
Duration of zero coupon bond that has seven years to maturity
The duration of a bond with a zero coupon rate is the same its maturity date. Thus the duration of the bond is 7 years
if the duration of maturity increases to 10 years, bo nd duration will be 10 years
if the maturity increases to 12 years, bond duration will be 12 years
PART 5
Repeat problem 39,assuming that the three bonds under consideration have 6 years to maturity.
a) At 8%
interest = 8% x 10000 = 800
1st 800 x 0.9259 = $740.74
2nd (800 + 10000) x 0.8573 = 9259.26
total = (9259.26 x 6) + 740.74 = $56296.3/10000 = 5.6 years
b) at 10%
interest = 10% x 10000 = 1000
1st 1000 x 0.9091 = $909.10
2nd (1000 + 10000) x 0.8264 = 9090.91
Total = (9090.91 x 6) + 909.1 = $55455.37/10000 = 5.5 years
c) coupon rate 12%
interest = 12% x 10000 = 1200
1st 1200 x 0.8929 = $1071
2nd (1071 + 10000) x 0.7972 = 8825.73
Total = (8825.73 x 6) + 1071= $54025.38/10000 =5.4 years
Investment Banks and Financial Institutions
PART 6
Repeat problem 41, assuming that the fair present value rose from $975 to $ 990
duration = 990/9.25 = 10.7 years
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