Question

A project that will provde annual cash flows of $2,750 for nine years costs $9,000 today. a. At a required return of 10 percent, what is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. At a required return of 29 percent, what is the NPV of the project? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. At what discount rate would you be indifferent between accepting the project and rejecting it? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) points eBook Hint 10.00 a. NPV $ b. NPV C. Discount rate % Print References 10

Answer 1

Answer

A	NPV	$6,837.25
B	NPV	-$475
C	Discount Rate	27%

Calculation of NPV (Net Present Value)

NPV = Present Value of cash inflows – Initial Investment

1. NPV when Discount rate is 10%

Since annual cash flows are equal we can use annuity method for calculating the NPV

Initial Investment = $9,000

Present Value of cash inflows = Yearly cash flow x Annuity factor for 9 years at 10%

                                                =$2,750 X 5.759

                                                =$15,837.25

NPV =$15,837.25 - $9,000

            =$6,837.25

                                   

2. NPV when Discount rate is 29%

Initial Investment = $9,000

Present Value of cash inflows = Yearly cash flow x Annuity factor for 9 years at 29%

                                                =$2,750 X 3.100

                                                =$8,525

NPV =$8,525 - $9,000

            = -$475

3. The discount rate at which accepting and rejecting of the project is indifferent

This indifferent rate is can be found out using IRR (Internal Rate of Return)

IRR is the rate at which NPV is Zero

NPV (r, -r NPV - NPV IRR r lower discount rate chosen higher discount rate chosen N NPV at r, NPV at r Ng

ra =10%

rb= 29%

Na=NPV@ ra = $6,837.25

Nb=NPV@ rb = -$475

( ra, rb, NPVa & NPV b are taken from above answers calculated)

IRR = 10 + ( ($6,837.25) / ($6,837.25 – (-$475)) )  x (29 – 10)

            = 27%

Proof

NPV When discount rate is 27%

Initial Investment = $9,000

Present Value of cash inflows = Yearly cash flow x Annuity factor for 9 years at 27%

                                                =$2,750 X 3.273

                                                =$9000

NPV =$9,000 - $9,000

            = 0