BFW2140 Corporate Finance S2, 2019: C C C C
BFW2140 Corporate Finance S2, 2019: C C C C
BFW2140 Corporate Finance S2, 2019: C C C C
S2, 2019
Evaluate: We can compute the price of a zero-coupon bond simply by computing the present value of
the face amount using the bond’s yield to maturity.
6-10 Plan: Given the yield, we can compute the price using Eq. 6.3. First, note that a 8.5% APR is equivalent
to a semiannual rate of 4.25%. Also, recall that the cash flows of this bond are an annuity of four
payments of $32.5, paid every six months, and one lump-sum cash flow of $1,000 (the face value), paid
in two years (four six-month periods).
Execute:
32.5 32.5 32.5 32.5 1,000
PV 963.91
0.085 0.085 2 3
0.085 0.085
4
1 1 1 1
2 2
2 2
Evaluate: The yield to maturity is the discount rate that equates the present value of the bond’s cash
flows with its price. By discounting the cash flows using the yield, we can find the bond’s price.
6-13 Plan: We can compute the bond’s coupon rate by rearranging Eq. 6.3 to find the coupon
payment. We can also use an annuity spreadsheet in Excel to find the coupon rate.
Execute:
C C C 1,000
897.33 C $32.83
(1 0.057) (1 0.057) 2
(1 0.057) 5
Evaluate: In order to compute the coupon rate, you must know the coupon payment. In this
case, we can solve for the coupon payment by rearranging Eq. 6.3 to find the annual coupon
payment and then dividing that number by the face value in order to convert the annual
payment into the coupon rate.
6-17 a. Because the yield to maturity is less than the coupon rate, the bond is trading at a premium.
52.3 52.3 52.3 1000
P $1,046.21
0.0954 0.0954 2
0.0954
14
1 1 1
2 2
2
b.
NPER Rate PV PMT FV Excel Formula
Given: 14 4.77% 52.3 1,000
Solve For (– =PV(0.0477,14,52.3,100
PV: 1,046.21) 0)
6-20 Plan: Because the first $70 coupon has just been paid, it no longer is reflected in the value of
the bond. The bond is now a nine-year maturity bond, which can be valued.
Execute: After the first coupon payment, the price of the bond will be
70 70 1,000
P $1,068.02.
(1 0.06) (1 0.06)9
6-25 a. Purchase price = 100 / 1.0430 = 30.83. Sale price = 100 / 1.0425 = 37.51. Return = (37.51 /
30.83)1/5 – 1 = 4.00%. I.e., since YTM is the same at purchase and sale, IRR = YTM.
b. Purchase price = 100 / 1.0430 = 30.83. Sale price = 100 / 1.0525 = 29.53. Return = (29.53 /
30.83)1/5 – 1 = -0.86%. I.e., since YTM rises, IRR < initial YTM.
c. Purchase price = 100 / 1.0430 = 30.83. Sale price = 100 / 1.0325 = 47.76. Return = (47.76 /
30.83)1/5 – 1 = 9.15%. I.e., since YTM falls, IRR > initial YTM.
d. Even without default, if you sell prior to maturity, you are exposed to the risk that the YTM
may change.
From Chapter 7: Problems 7-5, 7-6 and 7-18 (pages 248 to250)
Dividend yield is $7/$103 = 6.796% and capital gain rate is $10/$103 = 9.709%
7-18 Plan: Gillette’s dividend is expected to grow at 11.9% per year for five years and then at 1.5% per year
indefinitely. We should employ a two-stage growth model. First, we value the constant growth in
dividends five years from now and discount it to the present. Then we determine the value today of the
five dividend payments growing at 11.9% from year 1 to 5. The value of the stock today is the sum of
these two values.
0.66 1.119 5
PV15 1 $3.32
(0.076 0.119) 1.076
something wrong here since the answer is 3.32 and not 3.32. Perpetuity formula cannot be
applied when r-g is negative (0.076 0.119)
17.218
PV0 $11.937
(1.076)5
Evaluate: Gillette’s stock today is worth $15.257, which is the sum of $3.32 (the present value of the
first five dividends) and $11.937 (the present value of the dividends growing at 1.5% per year from year
6 onward).