Question

A company ,purchases a new machine with an initial cost of $15,000 and a salvage value of $1,800. Net revenues in year 1 are $ 8,000,$8,150 in year 2, and increase by $150 each year the following eight years. Use a MARR of 12% .

a. What is the annual worth ?

b. Determine the IRR of this machine

please show detailed and clear solution with or without using EXCEL.  thank you

Answer 1

We need to calculate the PW here. The interest rate is 12% and duration is 8 years.

a) PW = Cash Flow / (1+Interest Rate)^Duration

PW of the initial cost
-15000 / (1.12 ^ 0) = -15000

PW of the salvage value
1800 / (1.12 ^ 8) = 726.99

PW of the net revenue with gradient

8000 * (P/A, 12%, 8) + 150 * (P/G, 12%, 8)
= (8000 * 4.9676) + (150 * 14.4714)
= 39740.80 + 2170.71
= 41911.83

NPW = -15000 + 726.99 + 41911.83
NPW = 27638.82

Annual Worth = NPW / PW Annuity Factor

27638.82 / 4.9676 = 5563.82

b) The internal rate of return is the rate at which the value of the discounted cash flow equates to zero.

NPW = Cash Flow / (1+Interest Rate) ^ Duration

Cash Flow / (1+IRR) ^ Duration = 0

The IRR can be calculated using trial and error method or using Excel software.

If we choose interest rate of 15% then the NPV of the cash flow is $23359.10.
This is positive so we will raise the rate to 25% which gives us value of $13125.32

The interest rate of 55% has given us negative value of -421.61 which means it must little lower than 55%

Further, trials gave us the rate of 53.35%.

The IRR is 53.35%

Year	Cash Flow	PV @ 53.35%
0	-15000	-15000.00
1	8000	5216.82
2	8150	3465.69
3	8300	2301.58
4	8450	1527.99
5	8600	1014.10
6	8750	672.83
7	8900	446.28
8	10850	354.78
	NPW	0.08