Question

1. Assume a corporation is expecting the following cash flows in the future: $-6 million in year 1, $8 million in year 2, $19 million in year 3. After year 3, the cash flows are expected to grow at a rate of 4% forever. The discount rate is 8%, the firm has debt totaling $55 million, and 9 million shares outstanding. What should be the price per share for this company?

1a. As with most bonds, consider a bond with a face value of $1,000. The bond's maturity is 12 years, the coupon rate is 4% paid semiannually, and the discount rate is 10%. What is the estimated value of this bond today?

1b. As with most bonds, consider a bond with a face value of $1,000. The bond's maturity is 28 years, the coupon rate is 10% paid annually, and the discount rate is 16%. What is this bond's coupon payment?

1c. Assume that as an investor, you decide to invest part of your wealth in a risky asset that has an expected return of 22%, and a standard deviation of 12%. You invest the rest of your capital in the risk-free rate, which offers a return of 5%. You want the resulting portfolio to have an expected return of 6%. What percentage of your capital should you invest in the risky asset?

Answer 1

1) In order to calculate price per share, we need to know total market value of outstanding shares which cannot be computed from the given data.

1a) P.V. of given bond = 20/1.05^1/2 + 20/1.05 + 20/1.05^3/2 + 20/1.05^2 +20/1.05^5/2 + 20/1.05^3 + 20/1.05^7/2 + 20/1.05^4 + 20/1.05^9/2 + 20/1.05^5 + 20/1.05^11/2 + 20/1.05^6 + 20/1.05^13/2 + 20/1.05^7 + 20/1.05^15/2 + 20/1.05^8 + 20/1.05^17/2 + 20/1.05^9 + 20/1.05^19/2 + 20/1.05^10 + 20/1.05^21/2 + 20/1 = .05^11 + 20/1.05^23/2 + 1020/1.05^12 = $ 915.72

1b) P.V. of given bond's total coupon payment = 100/1.16 + 100/1.16^2 + 100/1.16^3 + 100/1.16^4 + 100/1.16^5 + 100/1.16^6 + 100/1.16^7 + 100/1.16^8 + 100/1.16^9 + 100/1.16^10 + 100/1.16^11 + 100/1.16^12 + 100/1.16^13 + 100/1.16^14 + 100/1.16^15 + 100/1.16^16 + 100/1.16^17 + 100/1.16^18 + 100/1.16^19 + 100/1.16^ 20 + 100/1.16^ 21 + 100/1.16^22 + 10//1.16^23 + 100/1.16^24 + 100/1.16^25 + 100/1.16^ 26 100/1.16^ 27 100/1.16^28 = $ 615.21

1c) Suppose if I invest 5% of my capital in risky asset; which means I invest remaining 95% of capital in risk free asset.

Expected return of resulting portfolio = (22% × 0.05) + (5% × 0.95) = 5.85%

Suppose if I invest 6% of capital in risky asset; which means I invest remaining 94% of capital in risk free asset.

Expected return of resultant portfolio = (22% × 0.06) + (5% × 0.94) = 6.02 ~ 6%

Therefore, 6% of total capital should be invested in risky asset.