Question

Park Co. is considering an investment that requires immediate payment of $29,480 and provides expected cash inflows of $8,900 annually for four years. Park Co. requires a 7% return on its investments. QS 24-3 Internal rate of return LO P4 1-a. What is the internal rate of return? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided. Round your present value factor to 4 decimals.)

Answer 1

Answer:

IRR = 13.8109 %

Explanation:

We can calculate the IRR using the following formula.

IRR = R1 + (NPV1 * (R2-R1) / (NPV1 - NPV2)

where,

R1 and R2 are random interest rates used to calculate 2 NPV values, and NPV1 is the higher npv value and NPV2 is the lower npv value among those calculated using R1 and R2.

Annuity factors for 4 years for,

R1 = 7% = 3.6243

R2 = 10% = 3.4869

Using the annuity factors, the present values are as follows

(8900 for 4 years is the cash flow generated)

Present Values:

R1 = 7% = 3.6243 * 8900 = $32,256.27

R2 = 10% = 3.4869 * 8900 = $31,033.41

Using these pv values, we subtract the initial out lay to compute Net present values,

NPV @ R1 of 7% = 32256.27 - 29480 = $2,776.27 = NPV1

NPV @ R2 of 10% = 31033.41 - 29480 = $1,553.41 = NPV2

Now we have the following information,

R1 = 7%

NPV1 = 2,776.27

R2 = 10%

NPV2 = 1,553.41

We input this data in the formula for IRR,

IRR = 7 + (2,776.27 * (10 - 7) ) / (2,776.27 - 1,553.41)

IRR = 7 + 6.8109

IRR = 13.8109 %

This is the rate at which NPV = 0.

Hope that helps.

Answer 2

Answer:

Year   Cashflow    DF@7%      PV           DF@10%     PV

               $                                 $                                  $

  0        (29,480)           1           (29,840)           1          (29,840)

1-4          8,900          3.3872    30,146         3.1699     28,212

                                        NPV   306                NPV      (1,628)

                                                     

IRR = LR     + NPV1/NPV1+NPV2    x (HR – LR)

IRR  = 7       + 306/306 + 1,628   x (10 – 7)

IRR = 7       + 306/1,934 x 3

IRR = 7       + 0.47

IRR = 7.47%

Explanation:

In this case, there is need to obtain the NPV at 7% discount rate. We also need to obtain the NPV at a higher rate since the first NPV is positive. Then, we will apply interpolation formula to determine the IRR. The cummulative discount factor used for the project can be obtained from present value of annuity factor at 7% and 10% respectively.