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Transcript of Mazboudi.fin86505 5
ASSIGNMENT 5- PROBLEMS 1
Assignment 5 – Problems
Ziad Y. Mazboudi
California Southern University
Corporate Finance
FIN 86505
Dr. Conrad Francis
ASSIGNMENT 5- PROBLEMS 2
Assignment 5 – Problems
Chapter 4, Question 10: Calculating Present Values. Imprudential, Inc. has an unfunded
pension liability of $750 million that must be paid in 25 years. To assess the value of the firm’s
stock, financial analysts want to discuss this liability back to the present. If the relevant discount
rate is 7 percent, what is the present value of this liability?
P=FVt/(1+r)^t (Jordan, Westerfield, & Ross, 2011, p. 143)
P= $750,000,000/(1+0.07)^25
P= $138,186,883.1
ASSIGNMENT 5- PROBLEMS 3
Chapter 4, Question 16: Calculating Rates of Return. Referring to the KVP security we
discussed at the very beginning of the Chapter:
a. What was the annual rate of return on investment in KVP in early January, 2010?
$1,000 on January 25, 2010 yields $2,000 on August 24, 2018
t = 8 years 7 months = 8.583 years
F =2 P
FVt = PVt (1+r)^t (Jordan et al., 2011, p. 133)
2= 1x(1+r)^8.583, solving for r
r = 8.41%
b. Suppose an investor invested Rs 1,000 in KVP on January 25, 2010, and
redeemed it three years later on January 24, 2013 , for Rs 1,100. What annual rate of return did
she earn?
FVt = PVt (1+r)^t
1,100 = 1000 (1+r)^3
1.1 = (1+r)^3 Solving for r
r = 3.23%
c. What would have been the value of the investment in KVP on January 24, 2013 if
she would have earned the annual rate of return calculated in part a?
FVt = PVt (1+r)^t
FV = 1000 (1.0841)^3
FV = 1,274.11 Rs
ASSIGNMENT 5- PROBLEMS 4
Chapter 4, Question 20: Calculating the Number of Periods. You expect to receive
$25,000 at graduation in two years. You plan on investing it at 9 percent until you have
$160,000. How long will you wait from now?
FV = $160,000
PV = $25,000
FVt = PVt (1+r)^t
$160,000 = $25,000 (1.09)^t
6.4 = 1.09^t solving for t
t = log 6.4/log 1.09
t = 21.54 years in 2 years
From now, it is T = 23.54 years
ASSIGNMENT 5- PROBLEMS 5
Chapter 5, question 4: Calculating Annuity Present Values. An investment offers $8,500
per year for 15 years, with the first payment occurring 1year from now. If the required return is 9
percent, what is the value of the investment?
PV = C x{1-[1/(1+r)^t]}/r (Jordan et al., 2011, p. 174)
C = $8,500
t = 15
r = 9%
PV15 = $8,500 x {1-[1/(1+0.09)^15]}/0.09
PV15 = $68,515.85
What would the value be if the payments occurred for 40 years?
PV40 = $8,500 x {1-[1/(1+0.09)^40]}/0.09
PV 40 = $91,437.56
What would the value be if the payments occurred for 75 years?
PV75 = $8,500 x {1-[1/(1+0.09)^75]}/0.09
PV75 = $94,297.15
What would the value be if the payments occurred forever?
PV = C/r (Jordan et al., 2011, p. 174)
PV = $8,500/0.09
PV = $94,444.44
ASSIGNMENT 5- PROBLEMS 6
Chapter 5, question 10: Calculating Perpetuity Values. Dawa Financial is trying to sell
you an investment policy that will pay you and your heirs $35,000 per year forever. If the
required return on investment is 7 percent, how much will you pay for the policy?
PV = C/r
PV = $35,000/0.07
PV = $500,000.00
ASSIGNMENT 5- PROBLEMS 7
Chapter 5, question 20: Calculating Loan Payments. You want to buy a new sports coupe
for $73,800, and the finance office at the dealership has quoted you a 6.1 percent APR loan for
60 months to buy the car. What will your monthly payments be?
PV = C x {1-[1/(1+r)t]}/r (Jordan et al., 2011, p. 174)
APR = 6.1%
r = 6.1/12 = 0.508% monthly
$73,800 = C x {1-[1/1.00508]^60]}/0.0058 solving for C
C = ($73,800 x 0.00508)/(1- [1/1.00508]^60)
C = 374.904/0.262
C= $1,430.93
What is the effective annual rate on this loan?
EAR = (1 + Quoted rate/m)m – 1 (Jordan et al., 2011, p. 176)
EAR = (1 + 0.061/12)12 – 1
EAR = 6.27%
ASSIGNMENT 5- PROBLEMS 8
Chapter 6, question 6: Bond Prices. App Store Co. issued 15-year bonds one year ago at a
coupon rate of 6.1 percent. The bonds make semiannual payments. If the YTM on these bonds is
5.4 percent, what is the current bond price?
Bond value = C x [1-1/(1+r)t]/r + F/(1+r)t (Jordan et al., 2011, p. 202)
Since App Store Co. issued the bonds a year ago, then we have 14 years remaining, hence
28 semiannual payments. t = 28
Since we have semiannual payments, then r= 5.4/2 = 2.7%
Since we have semiannual payments, then each coupon is 6.1/100 /2* 1,000 = $30.5
Solving for Bond Value = C x [1-1/(1+r)t]/r + F/(1+r)t (Jordan et al., 2011, p. 202)
Bond Value = $30.5 x [1 – 1/(1+0.027)28]/0.027 + $1,000/(1+0.027)28
Bond Value = $30.5 x 0.5257/0.027 + $474.27
Bond Value = $1,068.15
ASSIGNMENT 5- PROBLEMS 9
Chapter 6, question 16: Interest Rate Risk. Both Bond Xin and Bond Qan have 9 percent
coupons, make semiannual payments, and are priced at par value. Bond Xin has 3 years to
maturity, whereas Bond Qan has 20 years to maturity. If interest rates suddenly rise by 2 percent,
what is the percentage change in the price of Bond Xin? Of Bond Qan?
Coupon = 9 % with semiannual payments, means each payment is equal to $45
Since the bonds are priced at par value, this means that YTM=coupon rate = 9%
If interest rates suddenly rise by 2 percent, then the following is the new value of the
bonds, with YTM = 11%
PXin = $45 [1-1/(1+0.055)6]/0.055 + 1,000/1.0556
PXin = $45 * 4.9955 + $725.24
PXin = $950.04
Percentage change in price = (950.04-1000)/1,000 = -0.049956
Percentage price change for Bond Xin is -5%
PQan = $45 [1-1/1.05540/0.055 + 1,000/1.05540
PQan = $45 * 16.0461 + 117.46
PQan = $839.53
Percentage change in price = (839.53-1000)/1,000 = -0.16046
Percentage price change for Bond Qan = 16.05 %
If rates were to suddenly fall by 2 percent instead, what would the percentage change in
the price of Bond Xin be then? Of Bond Qan?
PXin = $45 [1-1/(1+0.035)6]/0.035 + 1,000/1.0356
PXin = $239.78 + $813.50
PXin = $1,053.28
ASSIGNMENT 5- PROBLEMS 10
Percentage change in price = (1,053.28-1000)/1,000 = 0.053
Percentage price change for Bond Xin is 5.3%
PQan = $45 [1-1/1.03540/0.035 + 1,000/1.03540
PQan = $960.98 + $252.57
PQan = $1,213.55
Percentage change in price = (1,213.55-1000)/1,000 = 0.2135
Percentage price change for Bond Qan = 21.35%
YTM 9 11 7 Δ(11-9)% Δ (7-9) %Xin $ 1,000.00 $ 950.04 $ 1,053.28 -4.996 5.33Qan $ 1,000.00 $ 893.53 $ 1,213.55 -10.647 21.36
One notices that the Qan bond with the longer maturity is more sensitive to interest rate
changes, in both direction, upward or downward.
ASSIGNMENT 5- PROBLEMS 11
Chapter 6, question 22: Using Bond Quotes. Suppose the
following bond quote for IOU Corporation appears in the financial
page of today’s newspaper. Assume the bond has a face value of
$1,000, and the current date is April 15, 2010. What is the yield
to maturity of the bond? What is the current yield?
Company (Ticker)
Coupon Maturity Last Price Last Yield EST Vol (000s)
IOU (IOU) 9.75 April 15, 2022 91.535 ?? 1,975
The Bond has 12 years to maturity so 24 payments of $48.75
The Bond price equation is: P = 48.75 [1-1/(1+ r)24]/r + 1000/(1+ r)24
Using Excel to calculate the YTM gives the following:
Settlement date 4/15/2010Maturity date 4/15/2022Annual coupon rate 0.0975Bond price (% of par) 91.535Face value (% of par) 100Coupons per year 2Yield to maturity 0.1104
So, the YTM = 11.04 %
The current yield is the annual coupon payment divided by the Bond price.
Current yield = $97.5/$91.35
Current yield =1.067%
ASSIGNMENT 5- PROBLEMS 12
Chapter 7, question 8. Valuing preferred stock. Gesto, Inc. has an issue of preferred
stock outstanding that pays a $4.50 dividend every year, in perpetuity. If this issue currently sells
for $84.70 per share, what is the required return?
P0 = D/R (Jordan et al., 2011, p. 241)
R = D/P = 4.5/84.70
R = 0.053
R = 5.3%
ASSIGNMENT 5- PROBLEMS 13
Chapter 7, question 14: Hot Wings, Inc., has an odd dividend policy. The company has
just paid a dividend of $8 per share and has announced that it will increase the dividend by $6
per share for each of the next four years, and then never pay another dividend. If you require a 15
percent return on the company’s stock, how much will you pay for a share today?
Since the company will not be paying any dividend after 4 years, then P4 = 0, then the
share today is equal to the total of the dividends over the next 4 years.
P0 = D1/(1+R) + D2/(1+R)2 + D3/(1+R)3 + D4/(1+R)4 (Jordan et al., 2011, p. 240)
P0 = $14/1.15 + $20/1.152 + $26/1.153 + $32/1.154
P0 = $62.69
ASSIGNMENT 5- PROBLEMS 14
Chapter 7, question 18: Finding the Dividend. Gontier Corporation stock currently sells
for $74.25 per share. The market requires an 11 percent return on the firm’s stock. If the
company maintains a constant 5.5 percent growth rate in dividends, what was the most recent
dividend per share paid on the stock?
Dividend grows at a steady rate, g, then the price can be written as:
P0 = D1/(R-g) = D0(1+g)/(R-g) (Jordan et al., 2011, p. 247)
D0 = P0 (R-g)/ (1+g) = $74.25 (0.11 – 0.055)/(1.055)
D0 = $3.87
ASSIGNMENT 5- PROBLEMS 15
References
Jordan, B. D., Westerfield, R. W., & Ross, S. A. (2011). Corporate Finance Essentials (7th ed.).
Singapore: The McGraw-Hill Companies.