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Chapter 6
Answers to Review Problems
Finance For Executives – 4th Edition
1. Future values.
a.
Time line:
Value at year-end 5 = FV($1,000)4 + FV($2,000)3 + FV($3,000)3 – FV($1,500)1
2. Present values.
Time line:
1 432 50
1 320
Using a calculator
Contract value =
32
)10.01(
M12$
)10.01(
M8$
)10.01(
M5$
M5$
Using a spreadsheet
3. Present values.
The investment is worth undertaking if its net present value is positive.
Time line:
Using a calculator
$5M
$5M
$8M
$12M
1 432 50
–$500,
–
$20,00
00
–
000
–
000
–
000
–
000 +
$100,
5432
)10.01(
000,250$
)10.01(
000,130$
)10.01(
000,130$
)10.01(
000,130$
)10.01(
000,130$
000,520$NPV
5432
)10.01(
000,250$
)10.01(
1
)10.01(
1
)10.01(
1
)10.01(
1
000,130$000,520$NPV
= $47,313
Using a spreadsheet
NPV is positive, so the machine should be purchased.
4. Buying a car.
a.
Time line of No Better Deals offer:
0
Time line of Best Deals offer:
The cash flows related to the two offers cannot be directly compared since they do not take place at the
same time. To make them comparable you have to imagine a financial transaction which, combined with
This financial transaction is straightforward: lend at 12 percent a $ amount at time zero, such that you will
2
)12.1(
000,6$
the Best Deals offer you would have to pay $4,000 to the dealer, get your car, and drive to your bank
where you would invest $5,237 at 12 percent. In two years time, you would go to your bank and take your
savings out. You would get exactly $6,000 that you would immediately give to Best Deals, as final
b.
Time line of New Best Deals offer:
We showed in part a. that the old Best Deals offer is equivalent to spending $8,783 at time zero. Using the
2
)12.1(
000,5$
12.1
000,3$
at the same time you get your car and pay $2,000 to the dealer. In one year time, you would go to the bank
and retrieve $3,000 that you would immediately turn to Best Deals. You would have to go again to the
0
1
2
0
1
2
c.
1. For No Better Deals, the present value of the 36 monthly payments must be equal to $10,000 at 0.5
percent per month. Since the present value of an annuity of $1 at 0.5 percent per period over 36 periods is
$, the monthly payments would have to be
22.304$
871.32
000,10$
.
2. The present value of 36 monthly payments of $302.71 when you can invest at 1 percent per month is
$9,114. This is the present value of 36 annuities of $302.71 at 1 percent per period over 36 periods. This
5. Saving for college.
Time line:
where X is the annual payment to the saving account.
Using a calculator
First, find the present value of $160,000 and second, using the annuity formula A6.1.2, compute the
annuity.
10
)04.01(
000,160$
From equation A6.1.2:
Annuity =
ADF
090,108$
19
32 10
0
$X $X $X $X $X $160,000
From Appendix 1:
11.8
04.
675564.01
ADF
So that:
11.8
090,108$
Using a spreadsheet
6. Saving for retirement.
a.
Time line ($ thousands):
where $In is the annual payment to the pension fund.
Using a calculator
To get $100,000 at the end of each year from the end of year 40 to the end of year 59, the amount that
0
1
2
3
39
40
41
42
58
59
The annual payment to the savings account from now to the end of year 39 is an annuity for which the
Using a spreadsheet
b.
The strategy to adopt depends upon your attitude towards risk. The 12 and 6 percent returns used in the
computations are based on historical average returns. These are returns that can be expected over a long
period of time. However, the probability that the investor will experience an actual return different from
