FI3300 – Fall 2006
Exam Two
Solutions
5) A $1,000 par value bond has coupon rate of 6% and the coupon is paid semi-annually. The bond
matures in 40 years and has a required rate of return of 10%. Compute the current price of this bond.
FV = 1000, PMT = (1000 x 0.06)/2 = 30 , N = 40 x 2 = 80, I/Y = 10/2 = 5.
CPT, then PV.
PV = - $608.07
Current price is $608.07.
6) A $1,000 par value bond sells for $1019.7694. It matures in 20 years, has a 10 percent coupon rate,
and pays interest semi-annually. What is the bond’s yield to maturity on a per annum basis (to 2 decimal
places)?
PV = -1019.7694, FV = 1000, N = 40, PMT = (0.1 x 1000)/2 = 50.
CPT, then I/Y = 4.8866
Yield to maturity = 4.8866 x 2 = 9.7732 = 9.77% p.a.
7) ABC Inc. just issued a twenty-year semi-annual coupon bond at a price of $1084.02. The face value of
the bond is $1,000, and the market interest rate is 9%. What is the annual coupon rate (in percent and
rounded to 2 decimal places)?
PV = -1084.02, FV = 1000, I/Y = 9/2 = 4.5, N = 40.
CPT, then PMT = 49.5659
Annual coupon rate = (49.5659 x 2)/1000 = 0.0991318 or 9.91% p.a.
8) Winshaw Manufacturing needs to raise $100,000,000 for an expansion project. The CFO is debating
whether to issue zero-coupon bonds or semi-annual coupon bonds. In either case the bonds would have
the SAME nominal required rate of return, a 30-year maturity and a par value of $1,000. If he issues the
zero-coupon bonds, they would sell for $212.56. If he issues the semi-annual coupon bonds, they would
sell for $1003.89. What annual coupon rate is Winshaw planning to offer on the coupon bonds? State your
answer in percentage terms, rounded to 2 decimal places.
[Hint1: Use annual compounding for the zero-coupon bonds and use semi-annual compounding for the
semi-annual fixed coupon bonds]
1
FI3300 – Fall 2006
Exam Two
Solutions
Find the required rate of return on the zero-coupon bonds.
FV=1000, N=30, PV=-212.56, PMT=0. CPT then I/Y.
The required rate of return on the zero-coupon bonds = 5.2973% p.a. (to 4 decimal places)
Use the required rate of return to solve for the semi-annual coupon payment.
FV=1000, N=60, PV = -1003.89, I/Y = 5.2973/2 = 2.64865. CPT then PMT.
PMT = 26.6166. This is the SEMI-ANNUAL payment.
To get the annual coupon rate, multiply PMT by 2 and then divide by the par value of $1000. Then
express answer as a percentage.
Coupon rate = (26.6166 x 2)/1000 = 0.0532332 or 5.32% p.a.
10) Davidson Company will pay an annual dividend of $6 per share one year from today. The dividend is
expected to grow at a constant rate of 15 percent permanently. The market requires 24 percent return on
the company. What is the current price of the stock (to 2 decimal places)?
Use the constant dividend growth model. D1 = 6, k = 0.24, g = 0.15.
Price = 6 / (0.24 – 0.15) = $66.67
12) The price of a stock in the market is $32. You know that the firm has just paid a dividend of $0.75 per
share (i.e., D0 = 0.75). The dividend growth rate is expected to be 6 percent forever. What is the investors’
required rate of return for this stock?
P = 32, D1 = 0.75 x (1.06) = 0.795.
Required rate of return = 0.795/32 + 0.06 = 0.02484 + 0.06 = 0.08484 or 8.48%
13) Brett Creative Media is expected to pay dividends at the end of the next three years of $0.5, $1.5, $2,
respectively. After three years, the dividend is expected to grow at a 5% constant annual rate forever. If
the required rate of return on this stock is 10%, what is the current stock price?
P3 = (2 x (1.05))/(0.10 – 0.05) = 42
At t=3, cash flow is 42 + 2 = 44
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FI3300 – Fall 2006
Exam Two
Solutions
Current stock price, P0
P0 
0.5
1.5
44


 34.75 (to 2 decimal places)
1
2
(1.10)
(1.10)
(1.10) 3
14) Appleby Administrative Services just paid a $4.00 annual dividend (that is, D0 = 4.00). Investors
believe that the firm will grow at 3% annually for the next 2 years and 2% annually forever thereafter.
Assuming a required return of 9%, what is the current price of the stock (to 2 decimal places)?
Here, you are given the growth rate and you need to work out the dividends.
1) Find t=1 dividend, D(t=1) = 4 x 1.03 = 4.12
2) Find t=2 dividend, D(t=2) = 4 x (1.03)2 = 4.2436
3) Find stock price at the end of t = 2. Use constant growth formula.
P2 = (4.2436 x 1.02)/(0.09-0.02) = 61.8353(keep up to 4 decimal places)
4) Cash flow at t= 2 is 61.8353 + 4.2436 = 66.0789
5) Stock price = 4.12/1.09 + 66.0789/(1.09)2 = $59.40 (to 2 decimal places)
FCB
2 years ago ABC Co. issued a 10 year, 5% semi-annual coupon bond. Its par value is $1,000. Investors
required 10% return rate. If the YTM has not changed since then, what should be the current price?
N=8x2=16, FV=1000, PMT=5%x1000/2=25, I/Y=10/2=5, so PV=-729.06
ZCB
Par value is $100, the current interest rate in the market is 9%, time to maturity is 15 years. How much is
the price?
FV=100, I/Y=9, n=15, PMT=0, PV=-27.45
Constant dividend growing model
The company just paid $3/share for dividend, and the market expects that the dividend with grow at 1%
annually forever. The discount rate is 10%. How much is the stock price?
Price=3x(1+0.01)/(0.1-0.01)=33.67
Non-constant dividend growing model
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FI3300 – Fall 2006
Exam Two
Solutions
The company just paid $2/share for dividend, and the market expects that the dividend with grow at 5%
annually for one year, then 3% for 3 years, and then will be of the same dollar amount forever. The
discount rate is 12%. How much will be the stock price after 1 year?
D1=2(1+0.05)=2.10
D2=D1(1+0.03)=2.163
D3=D2(1+0.03)=2.22789
D4=D3(1+0.03)=2.2947267
D5=D4=2.2947267
Starting from t=5, all dividend will be the same, so it is a perpetuity, therefore
P4=D5/(r-g)=2.2947267/(0.12-0)=19.1227
To find the price at t=1, we need to discount D2, D3, D4, and P4 back to t=1 (Not t=0), therefore,
P2=2.163/(1+0.12)1+2.22789/(1+0.12)2+2.2947267/(1+0.12)3+19.1227/(1+0.12)3
=1.93125+1.77606+1.63334+13.61116
=18.9518
4