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CHAPTER 6
DISCOUNTED CASH FLOW VALUATION
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
9.
Here we have the PVA, the length of the annuity, and the interest rate. We want to calculate the
annuity payment. Using the PVA equation:
PVA =
C
({1 – [1/(1 +
r)
]
t
} /
r
)
$30,000 =
C
{[1 – (1/1.08)
7
] / .08}
We can now solve this equation for the annuity payment. Doing so, we get:
C
= $30,000 / 5.20637 = $5,762.17
14.
For discrete compounding, to find the EAR, we use the equation:
EAR = [1 + (APR /
m
)]
m
– 1
So, for each bank, the EAR is:
First National:
EAR = [1 + (.1310 / 12)]
12
– 1 = .1392 or 13.92%
First United:
EAR = [1 + (.1340 / 2)]
2
– 1 = .1385 or 13.85%
Notice that the higher APR does not necessarily mean the higher EAR. The number of compounding
periods within a year will also affect the EAR.
20.
We first need to find the annuity payment. We have the PVA, the length of the annuity, and the
interest rate. Using the PVA equation:
PVA =
C
({1 – [1/(1 +
r)
]
t
} /
r
)
$61,800 = $
C
[1 – {1 / [1 + (.074/12)]
60
} / (.074/12)]
Solving for the payment, we get:
C
= $61,800 / 50.02385 = $1,235.41
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To find the EAR, we use the EAR equation:
EAR = [1 + (APR /
m
)]
m
– 1
EAR = [1 + (.074 / 12)]
12
– 1 = .0766 or 7.66%
21.
Here we need to find the length of an annuity. We know the interest rate, the PV, and the payments.
Using the PVA equation:
PVA =
C
({1 – [1/(1 +
r)
]
t
} /
r
)
$17,000 = $300{[1 – (1/1.009)
t
] / .009}
Now we solve for
t
:
1/1.009
t
= 1 – {[($17,000)/($300)](.009)}
1/1.009
t
= 0.49
1.009
t
= 1/(0.49) = 2.0408
t
= ln 2.0408 / ln 1.009 = 79.62 months
23.
Here we need to find the interest rate that equates the perpetuity cash flows with the PV of the cash
flows. Using the PV of a perpetuity equation:
PV =
C
/
r
$63,000 = $1,200 /
r
We can now solve for the interest rate as follows:
r
= $1,200 / $63,000 = .0190 or 1.90% per month
The interest rate is 1.90% per month. To find the APR, we multiply this rate by the number of
months in a year, so:
APR = (12)1.90% = 22.86%
And using the equation to find an EAR:
EAR = [1 + (APR /
m
)]
m
– 1
EAR = [1 + .0190]
12
– 1 = 25.41%
24.
This problem requires us to find the FVA. The equation to find the FVA is:
FVA =
C
{[(1 +
r)
t
– 1] /
r
}
FVA = $250[{[1 + (.10/12) ]
360
– 1} / (.10/12)] = $565,121.98
28.
Here the cash flows are annual and the given interest rate is annual, so we can use the interest rate
given. We simply find the PV of each cash flow and add them together.
PV = $2,800 / 1.0845 + $5,600 / 1.0845
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 Spring '08
 LAYISH
 Valuation

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