a. IRR Calculation: 0 = 9,400 + -4,500/(1+i)^1 + -3,100/(1.+i)^2 + -2400/(1+i)^3 + -100/(1+i)^4

To solve for i: Use Microsoft Excel's IRR function:

Step 1 Click on a cell, and type: =IRR(

Step 2 Select your year numbers and corresponding cash flows with 1 highighted box

Step 3 Click enter

IRR = 2%

b. If the appropriate discount rate is 10 percent, should you accept this offer?

To know whether or not to accept this offer, we need to know the net present value of the cash flows. The net present value is the sum of the present values from each cash flow of the investment/offer. If the net present value, NPV, of these cash flows when discounting at a 10% rate, is zero or negative, we should reject the offer. If the NPV is positive, we should accept it.

Yes. The net present value, which is the sum of the present values of each cash flow, is $876 when discounting each cash flow at a 10% rate.

Year Cash Flows($) Calculation Present Value @ 10%

0 $9,400 = 9,400 $9,400

1 -$4,500 = -4,500 / (1.10^1) -$4,091

2 -$3,100 = -3,100 / (1.10^2) -$2,562

3 -$2,400 = -2,400 / (1.10^3) -$1,803

4 -$100 = -100 / (1.10^4) -$68

Sum of Present Values, NPV = $876

c. If the appropriate discount rate is 20 percent, should you accept this offer?

To know whether or not to accept this offer, we need to know the net present value of the cash flows. The net present value is the sum of the present values from each cash flow of the investment/offer. If the net present value, NPV, of these cash flows when discounting at a 20% rate, is zero or negative, we should reject the offer. If the NPV is positive, we should accept it.

Yes. The net present value, which is the sum of the present values of each cash flow, is $2,060 when discounting each cash flow with a 20% rate.

Year Cash Flows($) Calculation Present Value @ 20%

0 $9,400 = 9,400 $9,400

1 -$4,500 = -4,500 / (1.10^1) -$3,750

2 -$3,100 = -3,100 / (1.10^2) -$2,153

3 -$2,400 = -2,400 / (1.10^3) -$1,389

4 -$100 = -100 / (1.10^4) -$48

Sum of Present Values, NPV = $2,060

d. What is the NPV of the offer if the appropriate discount rate is 10 percent? 20 percent?

To find the NPV with a 10% discount rate, we need to discount the cash flows by (1+10%) ^ Year #, and then sum each of the present values.

Note: the year # is the year in which the cash flows take place.

Present value at a 10% discount rate = $876,.

Present value at a 20% discount rate = $2,060

Year Cash Flows($) Calculation Present Value @ 10% Present Value @ 20%

0 $9,400 = 9,400 $9,400 $9,400 $9,400

1 -$4,500 = -4,500 / (1.10^1) -$4,091 -$3,750

2 -$3,100 = -3,100 / (1.10^2) -$2,562 -$2,153

3 -$2,400 = -2,400 / (1.10^3) -$1,803 -$1,389

4 -$100 = -100 / (1.10^4) -$68 -$48

Sum of Present Values, NPV = $876 $2,060

e. Are the decisions under the NPV rule in part (d) consistent with those of the IRR rule?

The IRR will give us the rate of return generated by the cash flows themselves, assuming a constant(over time) reinvestment return rate of each cash flow equal to the IRR. The NPV will give us the value of the stream of cash flows to us today, given we are discounting the cash flows by a specified discount rate. The discount rate can be thought of as the time value we are placing on the cash flows. Meaning, the greater the discount rate, the greater value we place on time, thus the less the future cash flows will be worth to us today.

Yes. Note: The first cash flow is income to us, as we take it in today at time 0. The following cash flows are expenses to us as we pay each out over the next four years. If we value money at a 10% annual rate, that means that each future cash flow will be worth less to us today than when we have to pay it out in the future. If we valued money at a 20% annual rate, these cash flows would be worth even more to us because we place an ever higher value on time. These decisions under NPV are consistent with those of the IRR rule. Note: the IRR is 2%. This means that the discount rate, or the amount placed on the time value of the cash flows, would have to be equal to (less than) 2% for the net present value of the future outgoing cash flows to be of equal to (less than) the amount taken in today, $9,400.