Tutorial Answers for Week 4 Workshop
Question 1
What happens to the future value of annuity if you increase the rate r? What happens
to the present value?
Assuming positive cash flows, the present value will fall and the future value will rise.
Question 2
An investment offers $3,600 per year for 15 years, with the first payment occurring
one year from now. If the required return is 10%, what is the value of the investment
today? What would be the value if the payments occurred for 40 years? For 75 years?
Forever?
Solution:
State the variables: C = $3,600, t = 15y, t = 40y, t = 75y, t = ∞, r = 10%
PVA = ?, PV perpetuity = ?
To find the present value of an annuity (
PVA
), we use the equation:
(
29
+

=
t
r
r
C
PVA
1
1
1
or
(
29
+

=
r
r
C
PVA
t
1
1
1
[email protected] yrs:
PVA = $3,600{[1 – (1/1.10)
15
] / .10} = $27,381.89
[email protected] yrs:
PVA = $3,600{[1 – (1/1.10)
40
] / .10} = $35,204.58
[email protected] yrs:
PVA = $3,600{[1 – (1/1.10)
75
] / .10} = $35,971.70
To find the PV of perpetuity, we use the equation:
r
C
PV
=
PV = $3,600 / .10 = $36,000.00
(Notice that as the length of the annuity payments increases, the present value of the
annuity approaches the present value of the perpetuity. The present value of the 75
year annuity and the present value of the perpetuity imply that the value today of all
perpetuity payments beyond 75 years is only $28.30.)
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First National Bank charges 12.2 percent compounded monthly on its business loans.
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 '09
 RezaMonem
 Accounting, Time Value Of Money, Net Present Value, Perpetuity, Mathematical finance

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