# 1. You have the following information on a project's cash flows. The cost of capital is 12.5%....

## Question:

1. You have the following information on a project's cash flows. The cost of capital is 12.5%.

Year Cash Flow
0 -$123,000 1 28,000 2 31,000 3 36,000 4 41,000 5 49,000 What is the NPV of the project? (round it two decimal places) What percent is the IRR? (round it to two decimal places) How many years is the payback? (round it to two decimal places) 2. A firm evaluates all of its projects by applying the IRR rule. The cash flows for a project is shown below and the firm requires 15% return on this type of project. First, compute the IRR of the project in box 1. (Do not include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16)) Then, make the investment decision based on the IRR by inputing either "accept" or "reject" in box 2. Year Cash Flow 0 -$36,500
1 21,000
2 17,000
3 7,000

3. A company estimates that its required rate of return is 18% on its capital investments. It is considering the following independent projects. Select all that are true.

It should reject Project E, which has an IRR of 18.5% with a payback of 11 years.

Project F, which has $439 NPV, must have an IRR that is higher than 18%. It should accept Project D, which requires an initial investment of$1,250,000 and generates a payback of 4.5 years.

It should accept Project B, which has an IRR of 16.5%.

It should accept Project C, which requires an initial investment of $1,000,000 and generates an IRR of 19%. It should accept Project A, which requires an initial investment of$145,000 and has a NPV of $1 ## NPV and IRR Net Present Value (NPV) is the sum of the present value of all future cash flows (positive and negative) over the entire life of a project or investment discounted back by the cost of capital of the project. NPV is used in the capital budgeting decisions, if NPV >0 it is considered that the project is financially viable, if NPV<o then it is not financially viable. The Internal Rate of Return (IRR) is the compounded annual rate of return that will be earned on a project or investment. It is calculated as the discount rate that makes the net present value (NPV) of a project zero. IRR is an investment analysis tool which is used to measure the feasibility of a project or investment. If the IRR is higher than the cost of capital of the project, the project is considered to be accepted, but in the other hand if the IRR is less than the cost of capital, the project should not be accepted ## Answer and Explanation: #### Answer of Question 1: • Calculation of NPV:  Year Cash Flow(CFn) Present Value (PVn = CFn/(1+r)^n where r= 12.5%, n = 0 to 5) NPV = Sum of All PV 0 -$ 1,23,000 -$1,23,000.00$ 4,454.28 1 $28,000$ 24,888.89 2 $31,000$ 24,493.83 3 $36,000$ 25,283.95 4 $41,000$ 25,596.10 5 $49,000$ 27,191.52

• Percent is the IRR: (round it to two decimal places)

Internal rate of Return is the Discounted Rates which make the NPV equals zero

{eq}NPV =0 =C1/(1+r)+C2/(1+r)^2 )+C3/(1+r)^3 +C4/(1+r)^4 +....+ Cn/(1+r)^n - A ..................(1) {/eq}

Where,

• C1,C2,.......,Cn = cash flow on nth Year
• A = initial investment
• n= tenure of investment
• r = Cost of Capital

Putting the Values in equation (1) we get,

{eq}0 = -$1,23,000+ ($ 28,000)/(1+r)^1+ ($31,000)/(1+r)^2 + ($ 36,000)/(1+r)^3 + ($41,000)/(1+r)^4 + ($ 49,000)/(1+r)^5 ...........(2) {/eq}

By solving the equation (2) for the value of r we get r = 13.83%

So IRR of the project = 13.83%

• However the IRR can be calculated using the financial calculators or Ms Excel (IRR Formula) or similar spreadsheet programs which is much faster process.

The syntax for IRR is:

IRR( range, {Guess} )

Guess - (optional) An estimate for expected IRR. Default is 0 .1 (10%).

• Calculation of payback period:
• We make the Cumulative cash flow table as below:

 Year Cash Flow(CFn) Cumulative Cash Flow 0 -$1,23,000 -$ 1,23,000 1 $28,000 -$ 95,000 2 $31,000 -$ 64,000 3 $36,000 -$ 28,000 4 $41,000$ 13,000 5 $49,000$ 62,000

• So payback period is somewhere between Year 3 and Year 4
• Considering the cash flow is symmetrical throughout the year

Payback Period = 3.68 Years

Putting the Cash flows in equation (1) again we get:

{eq}0 = -$36,500+ 21,000/(1+r)^1+ 17,000/(1+r)^2 + 7,000/(1+r)^3 .......(3) {/eq} By solving the equation (3) for r we get for r = 13.47% the RHS became Zero • So IRR of the project 13.47% • As IRR is lower than the required return of the project (15%) the project Should be rejected. #### 3. Answer of Question 3: • To select an investment which if financially feasible, the IRR should be higher than the cost of capital and the NPV of the Project should be positive. • In this context we should select the correct Options • It should reject Project E, which has an IRR of 18.5% with a payback of 11 years. (True) • Project F, which has$439 NPV, must have an IRR that is higher than 18%. (True)
• It should accept Project D, which requires an initial investment of $1,250,000 and generates a payback of 4.5 years. (False) • It should accept Project B, which has an IRR of 16.5%. (False) • It should accept Project C, which requires an initial investment of$1,000,000 and generates an IRR of 19%. (True)
• It should accept Project A, which requires an initial investment of $145,000 and has a NPV of$1 (True)