Case Assignment
1. Suppose you buy a bond that will pay $1000 in 10 years along with an annual coupon payment of $50. The interest rate is 4%. Answer the following questions:
A. What is the value of this bond?
B. Now suppose the bond has no coupon payments (it is a “zero coupon” bond) but still pays $1000 in 10 years. What is the value of this bond?
C. What would happen to the value of the bond if the inflation rate unexpectedly goes up? What if the bond value increases or decreases?
D. Now suppose the bond still pays an annual coupon of $50 but the interest rate drops to 2%. What is the new value of this bond?
2. The XYZ Corporation pays a dividend of $1 for each share, and its required rate of return is 8%. Answer the following questions:
A. Assuming zero growth in dividends, what is the value of each share?
B. Now assume a 4% annual growth rate in the dividend paid. What is the value of each share?
C. Assume the growth rate is still 4%, but the required rate of return drops to 6%. What is the new value of each share?
3. Acme Medical Corp. is expecting the cash flows from 2018-2022 shown in the table below. After 2022, it is expecting growth in cash flow at an annual rate of 3%. The firm has determined that its weighted average cost of capital (discount rate) is 7%. Using the table below, calculate the following:
A. What is the present value of Acme’s future cash flows using the discounted cash flow model?
B. If the firm has 200,000 common shares outstanding, zero preferred shares, and debt with a market value of $10,000,000, what would be the value of each share?
C. Now suppose the discount rate increases to 10%. How would your answers to a) and b) above change based on the new discount rate?
Year
Cash flow
2018
500,000
2019
550,000
2020
620,000
2021
700,000
2022
800,000
1. Suppose the Alpha Manufacturing Corporation is experiencing extreme financial difficulties and is considering bankruptcy. Its shareholders are currently almost equally divided about whether or not the company should go bankrupt, with one outspoken faction pushing for bankruptcy and the other strongly opposing it. The company has $50 million in debt—all in the form of bonds—and bondholders are pretty well united in wanting the firm to declare bankruptcy.
A. The CEO announces that he is leaning against bankruptcy. This means one faction of shareholders is happy, but another faction of shareholders is very upset, and the bondholders are also unhappy. Can the unhappy faction of shareholders team up with the bondholders to vote out the CEO? Explain your reasoning using references from the background readings.
B. Suppose Alpha ends up declaring bankruptcy. The company has no cash in the bank but owns $60 million worth of real estate and has only one type of shareholder—common shareholders. If Alpha sells the real estate, how much of the money will bondholders get, and how much with shareholders get? Explain your reasoning using references from the background readings.
C. Now suppose that Alpha has two classes of shareholders—common shareholders and preferred shareholders. Preferred shareholders are owed $20 million in dividends that have been unpaid in the past two years. If Alpha goes bankrupt and sells its $60 million worth of real estate, how much will bondholders get, how much will common shareholders get, and how much will preferred shareholders get? Explain your reasoning using references from the background readings.
This finance case asks you to value a coupon bond, a zero-coupon bond, the effect of rising inflation, and the bond at a lower rate, plus a dividend/stock valuation problem. Apply the present-value formulas and show your work.
Key takeaways
- Bond value = PV of coupons (annuity) + PV of face value.
- Zero-coupon bond = PV of face value only.
- Rising interest rates/inflation lower bond value (inverse relationship).
- Lower interest rate raises bond value.
- Show all computation steps.
A. The coupon bond
Value = present value of the $50 annual coupons for 10 years plus the present value of the $1000 face value, discounted at 4%. PV = 50 × [1 − (1.04)^−10]/0.04 + 1000/(1.04)^10 ≈ $405.54 + $675.56 ≈ $1,081.11. Show the steps.
B. Zero-coupon bond
With no coupons, value = 1000/(1.04)^10 ≈ $675.56.
C. Rising inflation
Explain the inverse relationship: if inflation (and thus interest rates) rises unexpectedly, the bond’s value decreases, because its fixed payments are discounted at a higher rate.
D. Lower interest rate (2%)
Recompute at 2%: value = 50 × [1 − (1.02)^−10]/0.02 + 1000/(1.02)^10 ≈ $449.13 + $820.35 ≈ $1,269.48 — higher, confirming the inverse rate-price relationship.
Stock/dividend part
For the dividend-valuation question, apply the dividend discount model (e.g., Gordon growth: P = D₁/(r − g)) and show your work.
Format
Show every calculation step for full/partial credit.
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