Question

Use the following information to answer the next three questions. Consider the following cash flows:

Year	Cash Flow
0	-$2,110,000
1	1,000,000
2	450,000
3	790,000
4	890,000

Assume a discount rate of 17.5 percent.

What is the payback period? Round your answer to two decimal places.

What is the net present value (NPV) rounded to the nearest dollar?

What is the internal rate of return?

please show work.

Answer 1

Part 1)

Payback period is the period within which the initial investment is recovered with the use of annual cash inflows. The payback period is calculated as below:

Year	Cash Flow	Cumulative Cash Flows
0	-2,110,000	-2,110,000
1	1,000,000	-1,110,000
2	450,000	-660,000
3	790,000	130,000
4	890,000	1,020,000

As can be seen from the above table that the cumulative cash flows turn positive from negative between Year 2 and Year 3. Therefore, the payback period will lie between these two years. The formula for calculating payback period is derived as below:

Payback Period = Years Upto which Partial Recovery of Initial Investment is Made + Balance Amount/Cash Flow of the Year in which Full Recovery is Made

Here, Years Upto which Partial Recovery of Initial Investment is Made = 2, Balance Amount = $660,000 and Cash Flow of the Year in which Full Recovery is Made = $790,000

Using these values in the above formula, we get,

Payback Period = 2 + 660,000/790,000 = 2.84 Years

_____

Part 2)

The NPV is the difference between the present value of cash outflows and cash inflows. It is calculated with the use of following formula:

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4

Substituting values in the above formula, we get,

NPV = -2,110,000 + 1,000,000/(1+17.5%)^1 + 450,000/(1+17.5%)^2 + 790,000/(1+17.5%)^3 + 890,000/(1+17.5%)^4 = $20,901.59

_____

Part 3)

IRR is the minimum rate of return acceptable from a project. It can be calculated with the use of IRR function/formula of EXCEL/Financial Calculator. The basic formula for calculating IRR is given as below:

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+IRR)^1 + Cash Flow Year 2/(1+IRR)^2 + Cash Flow Year 3/(1+IRR)^3 + Cash Flow Year 4/(1+IRR)^4

IRR is calculated with the use of EXCEL as follows:

where

IRR = IRR(B2:B6) = 18.01%