Question

You are required to use a financial calculator or spreadsheet (Excel) to solve 10 problems related to the risk and return, stocks and bonds valuation. You are required to show the following 3 steps for each problem:

(i) Describe and interpret the assumptions related to the problem.
(ii) Apply the appropriate mathematical model to solve the problem.
(iii) Calculate the correct solution to the problem.

1. A $1,000 par value 8-year bond with a 13 percent coupon rate recently sold for $980. What is the yield to maturity if the bond makes semiannual payments? Submit your answer as a percentage rounded to two decimal places.

2. Consider a 7 year bond with face value $1,000 that pays an 8.4% coupon semi-annually and has a yield-to-maturity of 6.9%. What is the approximate percentage change in the price of bond if interest rates in the economy are expected to increase by 0.40% per year? Submit your answer as a percentage and round to two decimal places. (Hint: What is the expected price of the bond before and after the change in interest rates?)

3. Nippon, Inc. expects its current annual $30 per share common stock dividend to remain the same for the foreseeable future. What is the intrinsic value of the stock to an investor with a required return of 9.2%? Round to two decimal places.

Answer 1

Solution:

1.

i. Since the bond makes semi-annual payments, the number of years would be 8*2 = 16, Coupon payment, C = 0.13/2*1000 = 65.

ii. We have C = 65, F = 1000, P = 980, n = 16 and YTM = ?

980 = 65 (PVIFA @ YTM, 16) + 1000 (PVIF @ YTM, 16)

Using excel,

=RATE(16,65,-980,1000,0)

= 6.71%

iii. Since 6.71% is semi-annually, the yield to maturity annually would be 6.71% x 2 = 13.42%.

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2.

i. Since the bond makes semi-annual payments, the number of years would be 7*2 = 14, Coupon payment, C = 0.084/2*1000 = 42. and YTM = 6.9%/2 = 3.45%

ii. We have C = 42, F = 1000, n = 14 and YTM = 3.45%

= 42 (PVIFA @ 3.45%, 14) + 1000 (PVIF @ 3.45%, 14)

Using excel,

=pv(3.45%,14,-42,-1000,0)

=$1,082.18

If interest rates increase by 40%, the new YTM is 6.9%+0.40% = 7.30%. The semi-annual YTM would be 7.30%/2 = 3.65%

= 42 (PVIFA @ 3.65%, 14) + 1000 (PVIF @ 3.65%, 14)

Using excel,

=pv(3.65%,14,-42,-1000,0)

= $1,059.46

Approximate percentage change in price of bond = ($1,059.46 - $1082.18)/1082.18 = -2.10%

iii. Hence, the approximate percentage change in price of bond is -2.10%.

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3.

i. For intrinsic value of stock, we use constant growth model,

ii. We have Stock per share = $30, Required return = 9.2%

Intrinsic value of stock = Stock per share/Required return

Intrinsic value of stock = $30/0.092

Intrinsic value of stock = $326.09

iii. The intrinsic value of stock is $326.09.