Question

Your cousin Mikey is attempting to sell you his portfolio to pay off some gambling debts. Vincent has informed Mikey that he needs the money by the end of the day or he will help him take a swim in the river. Mikey proposes to sell you his portfolio at a price of $100,000. Mikey’s portfolio includes the following:
a)40 zero coupon bonds with a $1,000 face value and 12 years to maturity. The YTM onthese bonds is 7.0% (assume annual compounding).
b)60 bonds with a $1,000 face value and a coupon rate of 5.0%. These bonds have 8 yearsto maturity and pay coupons on a semiannual basis. The YTM of these bonds is 6%.
c)120 shares of Hill Corp. stock. Hill Corp expects to pay a quarterly dividend of $1.50 in3 months, has a quarterly growth rate of 2%, and a required return of 4% per quarter.
How good of a deal is Mikey offering you for his portfolio? Clearly show your reasoning here with supporting calculations.

Answer 1

Value of zero coupon bond = FV / (1 + r)^n = 1,000 / (1 + 7%)^12 = $444.01

Value of coupon bond can be calculated using PV function

N = 8 x 2 = 16, PMT = 5% x 1000 / 2 = 25, FV = 1000, I/Y = 6%/2 = 3%

=> Compute PV = $937.19

Value of stock = D1 / (r - g) = 1.50 / (4% - 2%) = $75

Total Value of Mikey's portfolio = 40 x 444.01 + 60 x 937.19 + 120 x 75 = $79,617.15

Hence, the offer is great from Mikey's perspective but it is bad from your perspective as he is giving you assets which are worth a lot less than $100,000.