CHAPTER 6
DISCOUNTED CASH FLOW VALUATION
Answers to Concepts Review and Critical Thinking Questions
1.
The four pieces are the present value (PV), the periodic cash flow (
C
), the discount rate (
r
), and the number of
payments, or the life of the annuity,
t
.
2.
Assuming positive cash flows, both the present and the future values will rise.
3.
Assuming positive cash flows, the present value will fall and the future value will rise.
4.
It’s deceptive, but very common. The basic concept of time value of money is that a dollar today is not worth
the same as a dollar tomorrow. The deception is particularly irritating given that such lotteries are usually
government sponsored!
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.
6.
The better deal is the one with equal installments.
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.
Basic
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
PV@10% = $1,200 / 1.10 + $600 / 1.10
2
+ $855 / 1.10
3
+ $1,480 / 1.10
4
= $3,240.01
PV@18% = $1,200 / 1.18 + $600 / 1.18
2
+ $855 / 1.18
3
+ $1,480 / 1.18
4
= $2,731.61
PV@24% = $1,200 / 1.24 + $600 / 1.24
2
+ $855 / 1.24
3
+ $1,480 / 1.24
4
= $2,432.40
2.
To find the PVA, we use the equation:
PVA =
C
({1 – [1/(1 +
r)
]
t
} /
r
)
At a 5 percent interest rate:
X@5%:
PVA = $4,000{[1 – (1/1.05)
9
] / .05 } = $28,431.29
Y@5%:
PVA = $6,000{[1 – (1/1.05)
5
] / .05 } = $25,976.86
And at a 22 percent interest rate:
X@22%: PVA = $4,000{[1 – (1/1.22)
9
] / .22 } = $15,145.14
51