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 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
Basic
1.
PV@10% = $1,300 / 1.10 + $500 / 1.10
2
+ $700 / 1.10
3
+ 1,620 / 1.10
4
= $3,227.44
PV@18% = $1,300 / 1.18 + $500 / 1.18
2
+ $700 / 1.18
3
+ 1,620 / 1.18
4
= $2,722.41
PV@24% = $1,300 / 1.24 + $500 / 1.24
2
+ $700 / 1.24
3
+ 1,620 / 1.24
4
= $2,425.93
2.
X@5%:
PVA = $3,000{[1 – (1/1.05)
8
] / .05 } = $19,389.64
Y@5%:
PVA = $5,000{[1 – (1/1.05)
4
] / .05 } = $17,729.75
X@22%: PVA = $3,000{[1 – (1/1.22)
8
] / .22 } = $10,857.80
Y@22%:
PVA = $5,000{[1 – (1/1.22)
4
] / .22 } = $12,468.20
3.
FV@8%
= $900(1.08)
3
+ $1,000(1.08)
2
+ $1,100(1.08) + 1,200 = $4,688.14
FV@11%
= $900(1.11)
3
+ $1,000(1.11)
2
+ $1,100(1.11) + 1,200 = $4,883.97
FV@24%
= $900(1.24)
3
+ $1,000(1.24)
2
+ $1,100(1.24) + 1,200 = $5,817.56
4.
PVA@15 yrs:
PVA = $4,100{[1 – (1/1.10)
15
] / .10} = $31,184.93
PVA@40 yrs:
PVA = $4,100{[1 – (1/1.10)
40
] / .10} = $40,094.11
PVA@75 yrs:
PVA = $4,100{[1 – (1/1.10)
75
] / .10} = $40,967.76
PVA@forever:
PVA = $4,100 / .10 = $41,000.00
5.
PVA = $20,000 = $
C
{[1 – (1/1.0825)
12
] / .0825};
C
= $20,000 / 7.4394 = $2,688.38
6.
PVA = $75,000{[1 – (1/1.075)
8
] / .075} = $439,297.77;
can afford the system.
7.
FVA = $50,000 = $
C
[(1.062
5
– 1) / .062];
C
= $50,000 / 5.65965 = $8,834.47
8.
PV = $5,000 / .09 = $55,555.56
9.
PV = $58,000 = $5,000 /
r
;
r
= $5,000 / $58,000 = 8.62%
10.
EAR = [1 + (.12 / 4)]
4
– 1
= 12.55%
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