Question

Exercise 1 (Bond Valuation)

Zlw Inc. has decided to issue bonds to raise capital for a large-scale project that involves the construction of 24 new wind turbines in Tehachapi, CA.

(a) The bonds will have the following characteristics:

Annual coupons of $50

Face value of $1000

Maturity of 6 years

The required rate of return on the part of Zlw’s bondholders is 5%.

What is the value of the bonds?

(b) Assume instead (in this question only) that the maturity of the bonds is 7 years rather than 6. How does this change your answer in question (a)? Can you explain what is happening?

(c) Assume instead (in this question only) that the required rate of return on the part of the bondholders is 6%. How does this change your answer in question (a)? Can you explain what is happening?

(d) Assume instead (in this question only) that the required rate of return on the part of the bondholders is 4%. How does this change your answer in question (a)? Can you explain what is happening?

Exercise 2 (The Dividend Discount Model)

On September 4, 2020, Apple was trading at $120.96 per share. The stock was paying $0.82 in dividends per share. Assume (for simplicity) that dividend payments take place annually and the full $0.82 had just been paid. The cost of equity for Apple is 9.75%.

(a) If you believe that Apple will never grow its dividends, in other words, that the $0.82 will remain constant in perpetuity, then what is the value of the stock?

(b) If you believe that Apple’s dividends will grow at 6% per year forever, what is the value of the stock?

(c) If you believe that Apple’s dividends will grow at 9% per year forever, what is the value of the stock?

(d) If you believe that Apple’s dividends will grow at 9.5% per year forever, what is the value of the stock?

(e) What perpetual growth rate was the market assuming on September 4, 2020?

please write out steps

Answer 1

Note: Answered only the first question as per Chegg guidelines.

Exercise 1 (Bond valuation)

Part (a):

Value of the bond= $1,000

Part (b):

Value of the bond= $1,000

Value of the bond is the sum of present value of future cash flows (periodical coupon and redemption value), discounted at the rate of return required (YTM).

Since the rate of return required (YTM) is equal to coupon rate, value of the bond is equal to face value, irrespective of change in term to maturity.

Part (c):

Value of the bond= $950.83 (rounded)

Since the rate of return required (YTM) is higher than the coupon rate, value of the bond is less than its face value (bond at a discount)

Part (d):

Value of the bond= $1052.42 (rounded)

Since the rate of return required (YTM) is lower than the coupon rate, value of the bond is higher than its face value (bond at a premium).

Details of calculation as below: