Time July 1 2003 Oct 1 2003 Jan 1 2004 Apr 1 2004 July 1 2004 Oct. 1 2004 Jan 1
ID: 2442896 • Letter: T
Question
Time
July 1
2003
Oct 1
2003
Jan 1
2004
Apr 1 2004
July 1
2004
Oct. 1
2004
Jan 1
2005
Apr 1
2005
July 1
2005
Cost
$20k
4.5k
1.5k
1.5k
0
0
0
0
0
Benefit
0
3.5k
5.5k
4.5k
4.5k
4.5k
4.5k
4.5k
4.5k
If the capital cost within company is i=10% per year, and current date is July 1, 2005.
a) By using NPV, is this project worthwhile?
b) What is the project’s IRR?
Time
July 1
2003
Oct 1
2003
Jan 1
2004
Apr 1 2004
July 1
2004
Oct. 1
2004
Jan 1
2005
Apr 1
2005
July 1
2005
Cost
$20k
4.5k
1.5k
1.5k
0
0
0
0
0
Benefit
0
3.5k
5.5k
4.5k
4.5k
4.5k
4.5k
4.5k
4.5k
Explanation / Answer
a )The net cash flows have been discounted at 10%/4 =2.5% Costs Benefits Cash Flows PVF PV 0 20000 0 -20000 $1.00 ($20,000.00) 1 4500 3500 -1000 $0.98 ($975.61) 2 1500 5500 4000 $0.95 $3,807.26 3 1500 4500 3000 $0.93 $2,785.80 0 $0.00 4 0 4500 4500 $0.91 $4,076.78 5 0 4500 4500 $0.88 $3,977.34 6 0 4500 4500 $0.86 $3,880.34 7 0 4500 4500 $0.84 $3,785.69 8 0 4500 4500 $0.82 $3,693.36 NET PRESENT VALUE $5,030.96 Costs Benefits Cash Flows PVF PV 0 20000 0 -20000 $1.00 ($20,000.00) 1 4500 3500 -1000 $0.98 ($975.61) 2 1500 5500 4000 $0.95 $3,807.26 3 1500 4500 3000 $0.93 $2,785.80 0 $0.00 4 0 4500 4500 $0.91 $4,076.78 5 0 4500 4500 $0.88 $3,977.34 6 0 4500 4500 $0.86 $3,880.34 7 0 4500 4500 $0.84 $3,785.69 8 0 4500 4500 $0.82 $3,693.36 NET PRESENT VALUE $5,030.96b) NPV at 28% Costs Benefits Cash Flows PVF PV 0 20000 0 -20000 1.00 (20,000.00) 1 4500 3500 -1000 0.93 (934.58) 2 1500 5500 4000 0.87 3,493.75 3 1500 4500 3000 0.82 2,448.89 0 0.00 4 0 4500 4500 0.76 3,433.03 5 0 4500 4500 0.71 3,208.44 6 0 4500 4500 0.67 2,998.54 7 0 4500 4500 0.62 2,802.37 8 0 4500 4500 0.58 2,619.04 $69.49 At NPV 28%, the IRR is 69.49 almost equal to 0. Hence IRR is 28%. Costs Benefits Cash Flows PVF PV 0 20000 0 -20000 $1.00 ($20,000.00) 1 4500 3500 -1000 $0.98 ($975.61) 2 1500 5500 4000 $0.95 $3,807.26 3 1500 4500 3000 $0.93 $2,785.80 0 $0.00 4 0 4500 4500 $0.91 $4,076.78 5 0 4500 4500 $0.88 $3,977.34 6 0 4500 4500 $0.86 $3,880.34 7 0 4500 4500 $0.84 $3,785.69 8 0 4500 4500 $0.82 $3,693.36 NET PRESENT VALUE $5,030.96
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