For the project below, calculate the following using 10% as your cost of capital

ID: 2637344 • Letter: F

Question

For the project below, calculate the following using 10% as your cost of capital.

A) What is the payback period? 2, 3, 4, or 5 yrs.

B) What is the discount payback? 3.36, 4.15, 2.25, or 2.75 yrs.

C) What is the NPV of the project? $ 875.5, $ 1408.5, $ 1301.5, or $ 1245.5

D) What is the IRR of the project? 28.66%, 12.36%, 15.36%, or 35.14%

E) What is the MIRR of the project? 15.36%, 20.76%, 38.47%, or 28.66%

F) What is the profitability index of the project? 1.85, 1.52, .85, or 2.10

***May someone explain to me on how to solve these problems? Any help is appreciated. Thank you!***

Year: Profit: 0 -2500 1 750 2 1750 3 -500 4 3000

Explanation / Answer

ANSWER

A) Payback Period- The payback period is the length of time required to recover the initial cash outflow (initial Investment) on the project.

Here we need to calculate the time period required to recover initial investment of -2500 in year 0.

Initial cash outflow= no. of years took to recover the initial cash outflow

Since initial cash outflow is -2500 and sum of cash inflow for year 1 and 2 is 2500.

So Payback period is 2 years.

B) Discounted Payback Period- A major limitation of Payback Period is that it does not consider Time Value of Money. To overcome this limitation, the discounted payback period is used. In discounted payback period cash flows are first converted into their present values (by using suitable discounting rates) and then added to ascertain the calculation of discounted Payback period.

Calculation of discounted Payback period

Year

Cash flow

Present value=

cash flow/(1+r)t

Cumulative net cash flow after discounting

-2500

750

681.81

-1818.19

1750

1446.28

-371.91

-500

-375.66

-747.57

3000

2049.04

1301.47

Since initial outlay is recovered between 3rd and forth 4th year hence discounted payback period is 3.36 years.

C) NPV of the project-The NPV of the project is the sum of the present values of all the cash flows-positive as well as negative that are expected to occur over the life of the project.

NPV=?c/(1+r)^t -Initial investment

= -2500+681.82+1446.28+(-375.66)+2049.04

= 1301.48

Hence NPV of the project is 1301.5

D) IRR of the project-Internal rate of return(IRR) of a project is the discount rate which makes NPV equal to zero.

In other words it is the discount rate which makes the present value of all future cash flow equal to initial investment.

IRR is the value of r which satisfy the below equation.

Initial investment=? c/(1+r)^t

Calculation of IRR

-2500=750/(1+r)^1 +1750/(1+r)^2 +(-500)/(1+r)^3 +3000/(1+r)^4

By trial and error and trying all the given answers

28.66 is the IRR rate which satisfy the above equation.

E) MIRR of the project- There are many shortcomings to IRR rate such as when the cash flow of the project are not conventional (positive after initial investment)or when two or more projects are being compared to find out which one is best. In first case it is difficult to define what is IRR? And in the second case there are multiple IRR which is misleading. Further IRR cannot distinguish between positive and negative cash flows if it occur during project life. Also IRR is difficult to apply where short term interest rate differ from long term interest rates.

Then MIRR is the better option. MIRR is that rate which satisfy the below equation.

PVC=? TV/(1+MIRR)^n

Steps of calculate MIRR

PVC=? cash outflows/(1+r)^t
PVC=-2500+ (-500)/(1+0.10)^3

= - $2,876

TV=? cash inflows(1+r)^(n-t )
TV=750(1+0.10)^3+1750(1+.10)^2+3000

TV=6115.75

PVC=TV/(1+MIRR)^n
2876=6115.75/(1+MIRR)^4

After putting all options in the equation 20.76 makes the equation equal

hence MIRR= 20.76%

F) Profitability index of the project=present value of benefits/initial investment

= 3801.48/2500

=1.52

Decision criteria

>1 accept

=1 indifferent

<1 reject

Hence Profitability index of the project is 1.52 and accept the project