Download chapter 13 capital and financial markets

CHAPTER 13 – CAPITAL AND FINANCIAL MARKETS
ANSWERS TO EVEN-NUMBERED PROBLEMS
2. a.
Yes, you should approve the purchase of the inventory control software,
because the total present value of salary savings = $60,000/(1.07) +
$60,000/(1.07)2 + $60,000/(1.07)3 + $60,000/(1.07)4 = $203,232.68, which
exceeds the $200,000 purchase price.
b. The answer would change. You should not approve the purchase of the
inventory control software if the annual relevant discount rate is 9%, because
the total present value of salary savings would only be $194,383.19 (=
$60,000/(1.09) + $60,000/(1.09)2 + $60,000/(1.09)3 + $60,000/(1.09)), which
is less than the $200,000 purchase price.
c. The answer would change. You should not approve the purchase because the
total present value of salary savings, $203,232.68, is less than the $220,000
purchase price.
d. Compared to the answer in part (a), the answer would not change. You should
approve the purchase of the software, because the total present value of salary
savings = $60,000/(1.07) + $60,000/(1.07)2 + $60,000/(1.07)3 +
$60,000/(1.07)4 + $60,000/(1.07)5 + $60,000/(1.07)6 = $285,992.38, which
exceeds the $200,000 purchase price.
4. a. Your firm should purchase 2 computers, since the present value of each of the
first two computers is greater than their purchase price of $2600.
The present value of the first computer
= $3000/(1.1)1 + $3000/(1.1)2 + $3000/(1.1)3 = $7460.55
The present value of the second computer
= $2000/(1.1)1 + $2000/(1.1)2 + $2000/(1.1)3 = $4973.70
The present value of the third computer
= $1000/(1.1)1 + $1000/(1.1)2 + $1000/(1.1)3 = $2486.85
The present value of the fourth computer
= $500/(1.1)1 + $500/(1.1)2 + $500/(1.1)3 = $1243.43
b. Your firm should purchase 3 computers, since the present value of the first
three computers is greater than their purchase price of $2600.
The present value of the first computer
= $3000/(1.05)1 + $3000/(1.05)2 + $3000/(1.05)3 = $8169.79
The present value of the second computer
= $2000/(1.05)1 + $2000/(1.05)2 + $2000/(1.05)3 = $5446.50
The present value of the third computer
= $1000/(1.05)1 + $1000/(1.05)2 + $1000/(1.05)3 = $2723.25
The present value of the fourth computer
= $500/(1.05)1 + $500/(1.05)2 + $500/(1.05)3 = $1361.62
6.
8.
10.
The total value of your gold mine is $40,000 = (5 × $400)/0.05 = $2000/0.05.
a.
If the interest rate is 5%, this bond will sell for $100,000.
b.
If the interest rate is 10%, this bond will sell for $87,565.74.
If the discount rate is 10%, people will pay $100 per share ($100 = $10/0.10). If
people are uncertain about future profits they would pay less per share.
12. a. This would decrease the attractiveness of college. The costs would be the same,
but there would be fewer years of earnings and so the PV of future earnings
would be smaller.
b. This would decrease the attractiveness of college, as 1) the cost of going to
college would go up, because while in college you sacrifice higher earnings you
could be getting if employed full time and 2) the differential between high school
and college earnings would decrease, and therefore the PV of the stream of
differentials would decrease as well.
c. A higher interest rate makes future earnings less valuable today. The PV of
costs would change too, but the impact on the PV of future earnings would be
larger, because that stream extends much farther into the future. Therefore
permanently higher interest rates would make college less attractive.
14. In this case, the PV of costs would be $44,197 + $46,293/1.05 + $48,556/(1.05)2
+ $51,001/(1.05)3 = $176,384. Because the costs are assumed to come sooner in
this case, the PV of costs is larger than when they are assumed to occur at the end
of each year.
MORE CHALLENGING
16. a. None of the drugs should be developed. The present value of drug A, which
has the highest expected return, is PV = -$10 million + ($7 million/(1.30)2) +
($7 million/(1.13)3) = $ - 2,671,825. Note that we are discounting with 30%,
which is 10% interest on a risk-free asset and a 20% risk premium. Since the
drug has a negative present value, it should not be developed.
b. Again none of the drugs should be developed. Their present values are $ 220,931, $ -2,316,445, $-3,014,950 and $-4,441,960, respectively.
c. With an interest rate of 5%, and a two-year patent, again none of the drugs
should be developed. Their present values are $-1,936,000, $-3,664,000, $4.240,000 and $-5,392,000. With an interest rate of 5%, and a three-year
patent, only drug A should be developed, since it is the only one with a
positive present value of $931,200.
d. There is an inverse relationship between new drug development and the
interest rate, and a positive relationship between new drug development and
the duration of patent protection, as anticipated in answer to question 5e.