Name: ___________________________________
NetID: _______________________
Prof. Q. Ma, HAdm 2222 Fall 2009 HW2
1/6
HADM 2222 Fall 2009, Prof. Q. Ma
Homework assignment
#2
[Due 10 a.m. Wednesday, September 16, 2009, Statler 435 drop box]
1.
Seaborn Co. has identified an investment project with the following cash flows. If the discount rate is 10
percent, what is the present value of these cash flows? What is the present value at 18 percent? At 24
percent?
Year
Cash Flow
1
$1,100
2
720
3
940
4
1160
Solution:
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]% = $1,100 / 1.10 + $720 / 1.10
2
+ $940 / 1.10
3
+ $1,160 / 1.10
4
= $3,093.57
[email protected]% = $1,100 / 1.18 + $720 / 1.18
2
+ $940 / 1.18
3
+ $1,160 / 1.18
4
= $2,619.72
[email protected]% = $1,100 / 1.24 + $720 / 1.24
2
+ $940 / 1.24
3
+ $1,160 / 1.24
4
= $2,339.03
2.
Paradise, Inc., has identified an investment project with the following cash flows. If the discount rate is 8
percent, what is the future value of these cash flows in year 4? What is the future value at a discount rate
of 11 percent? At 24 percent?
Year
Cash Flow
1
$700
2
950
3
1,200
4
1,300
Solution:
To solve this problem, we must find the FV of each cash flow and add them. To find the FV of a
lump sum, we use:
FV = PV(1 +
r)
t
[email protected]% = $700(1.08)
3
+ $950(1.08)
2
+ $1,200(1.08) + $1,300 = $4,585.88
[email protected]% = $700(1.11)
3
+ $950(1.11)
2
+ $1,200(1.11) + $1,300 = $4,759.84
[email protected]% = $700(1.24)
3
+ $950(1.24)
2
+ $1,200(1.24) + $1,300 = $5,583.36
Notice we are finding the value at Year 4, the cash flow at Year 4 is simply added to the FV of
the other
cash flows. In other words, we do not need to compound this cash flow.
3.
An investment offers $4,600 per year for 15 years, with the first payment occurring one year from now.
If the required return is 8 percent, what is the value of the investment? What would the value be if the
payments occurred for 40 years? For 75 years? Forever?
Solution:

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*Name: ___________________________________
NetID: _______________________
Prof. Q. Ma, HAdm 2222 Fall 2009 HW2
2/6
To find the PVA, we use the equation:
PVA =
C
({1 – [1/(1 +
r)
]
t
} /
r
)
[email protected] yrs: PVA = $4,600{[1 – (1/1.08)
15
] / .08} = $39,373.60
[email protected] yrs: PVA = $4,600{[1 – (1/1.08)
40
] / .08} = $54,853.22
[email protected] yrs: PVA = $4,600{[1 – (1/1.08)
75
] / .08} = $57,320.99
To find the PV of a perpetuity, we use the equation:
PV =
C
/
r
PV = $4,600 / .08 = $57,500.00
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 $179.01.
4.

This is the end of the preview.
Sign up
to
access the rest of the document.