1. Question 1a
Given: We have a stock that will pay $14 per year with the next dividend paid later today. In 3 years, company can retain all earnings and earn 11% over the following year. Discount rate is 8%
What is the present value of the stock if it continues to be a cash cow?
PV= /.08 =189

2. Yes, because rate of return is greater than discount rate
Question 1b
Given: We have a stock that will pay $14 per year with the next dividend paid later today. In 3 years, company can retain all earnings and earn 11% over the following year. Discount rate is 8%
Should the company retain its earnings?
Yes, because rate of return is greater than discount rate
11% > 8%
Also, NPV>0 (see 1c)

3. Question 1c NPV=-14/1.08^3 + (14*1.11)/1.08^4 = .3087
Given: We have a stock that will pay $14 per year with the next dividend paid later today. In 3 years, company can retain all earnings and earn 11% over the following year. Discount rate is 8%
How much does the stock’s PV change if the company retains its earnings ?
NPV=-14/1.08^3 + (14*1.11)/1.08^4 = .3087

4. Question 2 March 8 2016: PV=Face/(1.0263)^30 500=Face/(1.0263)^30
We have a zero coupon bond sold for $500 on March When sold on the date, the YTM was 2.63%. The maturity date is March 8, 2046.
If the YTM on June was 2.51%, what did the bond sell for on this date?
March :
PV=Face/(1.0263)^30
500=Face/(1.0263)^30
Face=
June :
PV= / (1.0251)^29.75
PV=521.08

5. Question 3
Machine is purchased today for $5000. First maintenance cost is $50 two years from today. That cost is paid annually and grows 4% every year. Last maintenance cost is 9 years from today. What is the EAC if EAR is 10% and machine lasts 12 years?
PV of costs=
− − ∗ = =5273.9
EAC:
5273.9= 𝑋 .1 1− X=

6. Question 4 CAPM: Perp: 𝑟= 𝑟 𝑓 +𝛽 𝑟 𝑚 − 𝑟 𝑓
Stock currently sells for $50 and pays X dividend every year starting one year from today. The stock has a beta value of 1.5. Risk free rate is 5% and the risk premium is 6%. What is X?
CAPM:
𝑟= 𝑟 𝑓 +𝛽 𝑟 𝑚 − 𝑟 𝑓
𝑟= =.14 : Use this as the discount rate‼
Perp:
X/.14 = 50
X= 7

7. Question 5 Let X be proportion held by bondholders
Company gives stockholders expected rate of return of 20% if company is unlevered. company’s cost of debt is 12%. Stockholders are currently owning 25%. What fraction of the company’s value is held by bondholders?
Let X be proportion held by bondholders
.2 = .12X ( 1-X)
.13X=.05
X= .3846

8. Question 5
Company gives stockholders expected rate of return of 20% if company is unlevered. company’s cost of debt is 12%. Stockholders are currently owning 25%. What fraction of the company’s value is held by bondholders?
Also use M/M II
𝑟 𝑆 = 𝑟 0 + 𝐵 𝑆 𝑟 0 − 𝑟 𝑏
.25=.2+ 𝐵 𝑆 .2−.12
= 𝐵 𝑆
𝑆= , 𝐵= 5 13

9. Question 6
On July 5, 2013, Lauren borrowed 100,000. She financed the loan with equal monthly payments over 84 months, starting August 5, The SAR is 15% compounded month. On August 5, 2016, Lauren makes a balloon payment in addition to the regular payment. The loan has a .5% penalty charged on the amount of the balloon payment. What is the balloon payment?
1) Find monthly payment
100,000= 𝑋 − →→→→ 𝑋=
2) Find remaining regular balloon payment: payments= 47 payments left
𝐵𝑎𝑙𝑙𝑜𝑜𝑛= − =68,273.28
3) Total Payment = Balloon * = 68,614.28

10. Question 7
A stock is either $80 or $105 two years from today both with 50% probability. A European call option for this stock has an exercise price of $90 two years from today. If EAR is 14%, what is the most someone will be willing to pay for the option?
PV= .5∗ ∗ 105− =5.77
Willing to pay at most 5.77