Question

Please do not use Excel

2. A telecommunication company is investing $65,000 in a signal enhancing system. The system salvage value is 0 and MARR is equal to 18%.per year. The savings are shown in the following Table: End of Year Savings. $ 25,000 30,000 30,000 40,000 46,000 1. What is the Future Worth, FW? Is it good or bad project? 2. What is the IRR? 3. What is the discounted payback period for this project? 4. What is the payback period?

Answer 1

Initial Cost = 65,000

The savings are

Year 1 = 25,000

Year 2 = 30,000

Year 3 = 30,000

Year 4 = 40,000

Year 5 = 46,000

MARR = 18%

1. Future Worth of the Project

FW = -65,000 (F/P, 18%, 5) + 25,000 (F/P, 18%, 4) + 30,000 (F/P, 18%, 3) + 30,000 (F/P, 18%, 2) + + 40,000 (F/P, 18%, 1) + 46,000

FW = -65,000 (2.2878) + 25,000 (1.9388) + 30,000 (1.6430) + 30,000 (1.3924) + 40,000 (1.1800) + 46,000

FW = 84,025

The FW is greater than zero, the project is a good project.

2. Calculating the IRR using the trial and error method.

Let the rate of interest is 38%. Calculate the PW of the cash flows at 38%.

EOY	Cash Flows	Discounting Factor at 38%	Present Value
0	-65000	1.00000	-65000
1	25000	0.72464	18115.94
2	30000	0.52510	15752.99
3	30000	0.38051	11415.21
4	40000	0.27573	11029.19
5	46000	0.19980	9190.992
			504.3304

The PW is 504.33 and it’s a positive PW. So, increase the rate of interest to get a negative PW. Increase the rate of interest to 39% and calculate PW.

EOY	Cash Flows	Discounting Factor at 39%	Present Value
0	-65000	1.00000	-65000
1	25000	0.71942	17985.61
2	30000	0.51757	15527.15
3	30000	0.37235	11170.61
4	40000	0.26788	10715.21
5	46000	0.19272	8865.104
			-736.316

The PW is -736.32

Using interpolation

IRR = 38% + [504.33 – 0 ÷ 504.33 – (-736.32)] * 1%

IRR = 38.40%

The IRR is 38.40%

3. Discounted Payback Period

Year	CF	PV Factor	DCF	CCF
0	$-65,000	1	$-65,000	$-65,000
1	$25,000	0.85	$21,186.44	$-43,813.56
2	$30,000	0.72	$21,545.53	$-22,268.03
3	$30,000	0.61	$18,258.93	$-4,009.1
4	$40,000	0.52	$20,631.56	$16,622.45
5	$46,000	0.44	$20,107.02	$36,729.48

Payback Period = 3 + [-4009.1 – 0 ÷ 4009.1 – (16,622.45)] * 1 = 3.16 years

4. Simple Payback Period

Year	CF	NCF
0	$-65,000	$-65,000
1	$25,000	$-40,000
2	$30,000	$-10,000
3	$30,000	$20,000
4	$40,000	$60,000
5	$46,000	$106,000

Payback Period = 2 + (10,000 ÷ 30,000) = 2.33 years