Chapter 5: Discounted Cash Flow Valuation
Answers to Concepts Review and Critical Thinking Questions
1.
Assuming positive cash flows and a positive interest rate, both the present and the future
value will rise.
2.
Assuming positive cash flows and a positive interest rate, the present value will fall, and the
future value will rise.
4.
The most important consideration is the interest rate the lottery uses to calculate the lump
sum option. If you can earn an interest rate that is higher than you are being offered, you can
create larger annuity payments. Of course, taxes are also a consideration, as well as how
badly you really need $5 million today.
5.
If the total money is fixed, you want as much as possible as soon as possible. The team (or,
more accurately, the team owner) wants just the opposite.
7.
Yes, they should. APRs generally don’t provide the relevant rate. The only advantage is that
they are easier to compute, but, with modern computing equipment, that advantage is not
very important.
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems
require multiple steps. Due to space and readability constraints, when these intermediate
steps are included in this solutions manual, rounding may appear to have occurred.
However, the final answer for each problem is found without rounding during any step in
the problem.
1.
To solve this problem, we must find the PV of each cash flow and add them. To find
the PV of a lump sum, we use:
PV = FV / (1 +
r)
t
[email protected]% = $900 / 1.10 + $600 / 1.10
2
+ $1,100 / 1.10
3
+ $1,480 / 1.10
4
= $3,151.36
[email protected]% = $900 / 1.18 + $600 / 1.18
2
+ $1,100 / 1.18
3
+ $1,480 / 1.18
4
= $2,626.48
[email protected]% = $900 / 1.24 + $600 / 1.24
2
+ $1,100 / 1.24
3
+ $1,480 / 1.24
4
= $2,318.96
2.
To find the PVA, we use the equation:
PVA =
C
({1 – [1/(1 +
r)
]
t
} /
r
)
1

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*Sign up*At a 5 percent interest rate:
[email protected]%:
PVA = $4,000{[1 – (1/1.05)
9
] / .05 } = $28,431.29
[email protected]%:
PVA = $6,000{[1 – (1/1.05)
5
] / .05 } = $25,976.86
And at a 22 percent interest rate:
[email protected]%: PVA = $4,000{[1 – (1/1.22)
9
] / .22 } = $15,145.14
[email protected]%: PVA = $6,000{[1 – (1/1.22)
5
] / .22 } = $17,181.84
Notice that the PV of Cash flow X has a greater PV at a 5 percent interest rate, but a
lower PV at a 22 percent interest rate. The reason is that X has greater total cash
flows. At a lower interest rate, the total cash flow is more important since the cost of
waiting (the interest rate) is not as great. At a higher interest rate, Y is more valuable
since it has larger cash flows. At a higher interest rate, these bigger cash flows early
are more important since the cost of waiting (the interest rate) is so much greater.
3.

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