Question

Please show work for every part of the question

Bob is considering investing in one of the following investment projects.

                           A                 B                  C                 D

Initial cost         100               130                 200            330

Annual Income   148               130.78            185            184.55

Annual Cost       123.62            92                 137.52          93

Each alternative has a 5 year useful life.

What is the rate of return for alternative A?

What is the rate of return for alternative B?

What is the rate of return for alternative C?

What is the rate of return for alternative D?

If Bob requires at least an 8% return on his investments,what is the incremental rate of return between the choices left?

Which alternative should he select?

Answer 1

For Alternate A:

IRR = when Present value of all the cash inflows is equal to initial investment

Initial investment = $100

Net Cash Annual Flow = $148 - $123.62 = $24.38

Number of Cash flows = 5

We can use Financial Calcuclator to find IRR., Just follow the steps:

Press CF then 2nd button and then CE/C: This will clear memory of the calculator.

Now Enter -100 as CF0, and then press down arrow button.

Now Enter CF1 to CF5 to the value of 24.38

Now press IRR button on your calculator and then press CPT button.

You will get the IRR,

Hence IRR of Alternate A = 6.9861%

Now repeat the same procedure for Alternate B, C and D.

Rater of return for Alternative "B"'

Initial investment = $130

Net Cash Annual Flow = $130.78 - $92 = $38.78

Number of Cash flows = 5

We can use Financial Calcuclator to find IRR., Just follow the steps:

Press CF then 2nd button and then CE/C: This will clear memory of the calculator.

Now Enter -130 as CF0, and then press down arrow button.

Now Enter CF1 to CF5 to the value of 38.78

Now press IRR button on your calculator and then press CPT button.

You will get the IRR,

Hence IRR of Alternate "B" = 15%

Rate of Return for Alternative "C"

Initial investment = $200

Net Cash Annual Flow = $185 - $137.5 = $47.5

Number of Cash flows = 5

We can use Financial Calcuclator to find IRR., Just follow the steps:

Press CF then 2nd button and then CE/C: This will clear memory of the calculator.

Now Enter -200 as CF0, and then press down arrow button.

Now Enter CF1 to CF5 to the value of 47.5

Now press IRR button on your calculator and then press CPT button.

You will get the IRR,

Hence IRR of Alternate "C" = 6.02%

Rate of Return for Alternative "D"

Initial investment = $330

Net Cash Annual Flow = $184.55 - $93 = $91.55

Number of Cash flows = 5

We can use Financial Calcuclator to find IRR., Just follow the steps:

Press CF then 2nd button and then CE/C: This will clear memory of the calculator.

Now Enter -330 as CF0, and then press down arrow button.

Now Enter CF1 to CF5 to the value of 91.55

Now press IRR button on your calculator and then press CPT button.

You will get the IRR,

Hence IRR of Alternate "D" = 12%

If Bob requires 8% raturn on his investments. Incremental rate of return between choices:

Alternative - A
Year	Income	Cost	NAB	PV factor at 8%	Discounted NAB
	(A)	(B)	(C)=(A)-(B)	(D)	(C)x(D)
0		100	-100	1	-100
1	148	123.62	24.38	0.9259	22.573442
2	148	123.62	24.38	0.8573	20.900974
3	148	123.62	24.38	0.7938	19.352844
4	148	123.62	24.38	0.735	17.9193
5	148	123.62	24.38	0.6806	16.593028
				Present Value	-2.660412
Alternative - B
Year	Income	Cost	NAB	PV factor at 8%	Discounted NAB
	(A)	(B)	(C)=(A)-(B)	(D)	(C)x(D)
0		130	-130	1	-130
1	130.78	92	38.78	0.9259	35.906402
2	130.78	92	38.78	0.8573	33.246094
3	130.78	92	38.78	0.7938	30.783564
4	130.78	92	38.78	0.735	28.5033
5	130.78	92	38.78	0.6806	26.393668
				Present Value	24.833028
Alternative - C
Year	Income	Cost	NAB	PV factor at 8%	Discounted NAB
	(A)	(B)	(C)=(A)-(B)	(D)	(C)x(D)
0		200	-200	1	-200
1	185	137.53	47.47	0.9259	43.952473
2	185	137.53	47.47	0.8573	40.696031
3	185	137.53	47.47	0.7938	37.681686
4	185	137.53	47.47	0.735	34.89045
5	185	137.53	47.47	0.6806	32.308082
				Present Value	-10.471278
Alternative - D
Year	Income	Cost	NAB	PV factor at 8%	Discounted NAB
	(A)	(B)	(C)=(A)-(B)	(D)	(C)x(D)
0		330	-330	1	-330
1	184.55	93	91.55	0.9259	84.766145
2	184.55	93	91.55	0.8573	78.485815
3	184.55	93	91.55	0.7938	72.67239
4	184.55	93	91.55	0.735	67.28925
5	184.55	93	91.55	0.6806	62.30893
				Present Value	35.52253

From the above calculations, we have found the net present value of all the alternatives.

The Present Worth of Alternative "D" is highest with $35.53.

Hence Alternative D should be selected.