In: Economics
A. What is the ERR for this project? Assume that MARR = 15% per year. Is this project considered to be profitable?
Investment cost |
$15,000 |
Expected life |
7 years |
Market (salvage) |
–$1,500a |
Annual receipts |
$8,750 |
Annual expenses |
$3,550 |
a A negative market value means that there is a net cost to dispose of an asset. |
B. What is the discounted payback period?
*Answer:
*a)
We will have to calculate the discounted values of the
outflow.
PV = Cash Flow / (1+Interest Rate)^Duration
Outflow
PV of Investment Cost = 15000
PV of Annual Expenses
=PV(15%,7,-3550)
= 14769.49
Salvage value has a negative sign which means it is an
outflow
1500 / (1.15)^7 = 563.91
FV of Outflow = 30333.40
Now we need FV of the inflow
FV = Cash Flow * (1+Interest Rate)^Duration
=FV(15%,7,-8750)
= 96834.49
Now we need the interest rate which equate these two values
96834.49 / 30333.40 = 3.1923
3.1923 ^ (1/7) = 1.1804
(1.1804 - 1) * 100 = 18.04%
The ERR is greater than MARR so the project is justified.
*b)
We will have to discount the cash flow
PV = Cash Flow /(1+Interest Rate)^Duration
The PV and cumulative cash flow is given in the table below
Year | Cash Flow | PV @ 15% | Cumulative |
0 | -15000 | -15000 | -15000.00 |
1 | 5200 | 4521.74 | -10478.26 |
2 | 5200 | 3931.95 | -6546.31 |
3 | 5200 | 3419.08 | -3127.23 |
4 | 5200 | 2973.12 | -154.11 |
5 | 5200 | 2585.32 | 2431.21 |
6 | 5200 | 2248.1 | 4679.31 |
7 | 3700 | 1390.97 | 6070.28 |
The cumulative cash flow has turned positive in the 5th year
4+ (154.11 / (154.11+2431.21))
= 4 + 0.0596
= 4.0596 or 4.06 Years.
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