Question

Question 3. A project has an estimated annual cash flow of $9,500 for the first 10 years, and $11,000 for the next 10 years. The company’s WACC is 9% and IRR is 13%.

a.) What is the project’s payback?

b.) What is the project’s NPV?

Answer 1

Requirement-(a The Payback period (nothing but the traditional or conventional recovery period) is the period within which, cash outflows associated with the project can be recovered by the management but without considering time value of money. The answer is expressed in terms of number of periods (may be weeks or months or years, etc.). To calculate the payback period, initial investment in year-0 is required. However, it is not given in the question. Still, a clue is given in the question to calculate the initial cash outflow that project's IRR is 13%. IRR stands for Internal Rate of Return which is the discount rate that makes project's future cash equals to initial investment or in other words, IRR is the rate which makes NPV equals to zero. Therefore, IRR assumes that the future cash flows are invested in the project at the IRR otherwise, project's NPV cannot become zero when future cash flows are discounted to current worth using the IRR. Therefore,

Present Year PVF @ 13% EXCEL SCREENSHOT: OW Value 9,500 0.88496 $8,407.08 9,500 0.78315 $7,439.89 0.69305 $6,583.98 9,500 0.61332 $5,826.53 $9,500 0.54276 $5,156.22 $9,500 0.48032 $4,563.03 7 $9,500 0.42506 $4,038.08 9,500 0.37616 $3,573.52 9,500 0.33288 $3,162.41 10 $9,500 0.29459 $2,798.59 11 $11,000 0.26070 $2,867.67 12 $11,000 0.23071 $2,537.76 13 $11,000 0.20416 $2,245.81 14 $11,000 0.18068 $1,987.44 15 $11,000 0.15989$1,758.80 16 $11,000 0.14150 $1,556.46 17 $11,000 0.12522 $1,377.40 18 $11,000 0.11081$1,218.94 19 $11,000 0.09806 $1,078.70 20 $11,000 0.08678 $954.61 2 Present $9,500 Year Cash Flow PVF 13% Value 4 9500 9500 9500 9500 9500 9500 9500 9500 9500 9500 11000 11000 11000 11000 11000 11000 11000 11000 11000 11000 1/(1+1396) -c3/(1+1396) -C4/(1+1396) -C5/(1+1396) -С6/(1+1396) -C7/(1+13%) -C8/(1+1396) -c9/(1+1396) -C10/(1+13%) -C11/(1+1396) -C12/(1+1396) -C13/(1+1396) -C14/(1+1396) -C15/(1+1396) -C16/(1+1396) -C17/(1+136) -c18/(1+1396) -c19/(1+1396) -C20/(1+1396) -C21/(1+13%) B4 *C4 B10*C10 =B11*C11 B12*C12 =B13*C13 =B14*C14 B16 C16 -B17 C17 -B18 C18 -B19 C19 -B20 C20 =B21*C21 -B22"C22 Initial Investment-SUM(D3:D22 Initial Investment $69,132.90'

Now, considering $69,132.90 as the initial investment, Payback period shall be calculated as below: in case of equal annual cash flow, Payback Period- Initial investment/ Annual Cash Initial investment $69,132.90 Annual Cash Flows $9,500 Payback Period .28 years ($69,132.90/$9,500]

Requirement-(b In order to calculate NPV of the given cash flows, Future cash flows must be discounted to current worth (using WACC of 9%) so that present value of future cash flows can be calculated. From the present value of future cash flows calculated, initial investment shall be deducted for calculating Net Present Value (NPV).

Present Year PVF @ 9% EXCELL SCREENSHOT: OW Value 0.91743 8,715.60 $9,500 0.84168 $7,995.96 $9,500 0.77218 $7,335.74 0.70843$6,730.04 $6,174.35 0.59627 $5,664.54 7 $9,500 0.54703 $5,196.83 9,500 0.50187 $4,767.73 9,500 0.46043 $4,374.06 0.42241 $4,012.90 11 $11,000 0.38753 $4,262.86 12 $11,000 0.35553 $3,910.88 0.32618 $3,587.97 0.29925 $3,291.71 0.27454 $3,019.92 16 $11,000 0.25187$2,770.57 17 $11,000 0.23107$2,541.80 0.21199 $2,331.93 9$2,139.39 1,962.74 Present Value of future Cash flows $90,787.52 $9,500 2 Year Cash Flow PVF 9% Value 4 9500 9500 9500 9500 9500 9500 9500 9500 9500 9500 11000 11000 11000 11000 11000 11000 11000 11000 11000 11000 -1/(1+996) 500 500 0.64993 -C3/(1+996) C4/(1+96) =C5/( 1 +996) -С6/(1+996) -C7/(1+96) -С8/( 1 +996) -C9/(1+996) B4 C4 10 $9,500 -B10* C10 B11 C11 =B12*C12 -B13 C13 B14 C14 =B15*C15 -B16*C16 -817"С17 B18 C18 -819°C19 -B20 C20 B21 C21 B22*C22 10/(1+996) C11(1+996) =C12/(1+996) -C13/(1+996) C14(1+996) -C15/(1+996) C16/(1+996) -C17/(1+96) C18/(1+996) -C19/(1+996) -C20/(1+996) -C21/(1+9%) 13 $11,000 14 $11,000 15 $11,000 18 $11,000 19 $11,000 20 $11,000 0.17843 Present Value of future cash flows-SUM(D3:D22) Less: Initial investment in year-0-$69,132.90 [As calculated in Requirement-(a) using IRR of 1396)] Net Present Value (NPV) $21,654.61