A. What is the ERR for this project? Assume that MARR = 15% per year. Is...

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)	–$1,500^a
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?

Expert Solution

*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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Rahul Sunny answered 8 months ago

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