Question

Bellinger Industries is considering two projects for inclusion in its capital budget, and you have been asked to do the analysis. Both projects' after-tax cash flows are shown on the time line below. Depreciation, salvage values, net operating working capital requirements, and tax effects are all included in these cash flows. Both projects have 4-year lives, and they have risk characteristics similar to the firm's average project. Bellinger's WACC is 10%.

	0		1		2		3		4
Project A	-950		700		390		210		260
Project B	-950		300		325		360		710

What is Project A's payback?

What is Project A's discounted payback?

What is Project B's payback?

What is Project B's discounted payback?

Answer 1

Payback period is the time required for the operating cash inflows to recover the initial investment in a project.

For Project A:

Payback period calculation:

Here, initial investment = $950

Cumulative cash flows after year 1 = $700

Cumulative cash flows after year 2 = $700 + $390 = $1090

The cumulative cash flows reach the initial investment amount of $950 sometime in year 2.

Therefore the payback period would be more than 1 years and less than 2 years. Steps in the calculation of payback period are given below:

a. Amount of cash flow in year 2 needed to reach $950 cumulative cash flows:

$950 - $700 (year 1's cumulative cash flow amount) = $250

b. Percentage of year 2 until cumulative amount of $950 is reached:

$250 / $390 = 0.6410

c. Payback period = 1 + 0.6410 = 1.6410 years

Discounted payback period calculation:

First we will calculate the present value of cash flows. We will use the present value of $1 table to find the required present value. Present value of $1 at 10% for various years is 0.909, 0.826, 0.751, 0.623 respectively.

Now, we will calculate the present value of the cash flows by multiplying the cash flows with their respective present values as per below:

Year 1 : $700 * 0.909 = $636.3

Year 2 : $390 * 0.826 = $322.14

Year 3 : $210 * 0.751 = $157.71

Year 4 : $260 * 0.623 = $161.98

Now, we will calculate the cumulative present value (PV) of cash flows as per below:

Cumulative PV cash flows after year 1 = $636.3

Cumulative PV cash flows after year 2 = $636.3 + $322.4 = $958.7

The cumulative PV cash flows reach the initial investment amount of $950 sometime in year 2.

Therefore the discounted payback period would be more than 1 year and less than 2 years. Steps in the calculation of payback period are given below:

a. Amount of cash flow in year 2 needed to reach $950 cumulative cash flows:

$950 - $636.3 (year 1's cumulative cash flow amount) = $313.7

b. Percentage of year 2 until cumulative amount of $950 is reached:

$313.7 / $322.14= 0.97

c. Payback period = 1 + 0.9738 = 1.97 years

For Project B:

Payback period calculation:

Here, initial investment = $950

Cumulative cash flows after year 1 = $300

Cumulative cash flows after year 2 = $300 + $325 = $625

Cumulative cash flows after year 2 = $300 + $325 + $360 = $985

The cumulative cash flows reach the initial investment amount of $950 sometime in year 3.

Therefore the payback period would be more than 2 years and less than 3 years. Steps in the calculation of payback period are given below:

a. Amount of cash flow in year 3 needed to reach $950 cumulative cash flows:

$950 - $625 (year 2's cumulative cash flow amount) = $325

b. Percentage of year 3 until cumulative amount of $950 is reached:

$325 / $360 = 0.9027

c. Payback period = 2 + 0.9027 = 2.9027 years

Discounted payback period calculation:

First we will calculate the present value of cash flows. We will use the present value of $1 table to find the required present value. Present value of $1 at 10% for various years is 0.909, 0.826, 0.751, 0.623 respectively.

Now, we will calculate the present value of the cash flows by multiplying the cash flows with their respective present values as per below:

Year 1 : $300 * 0.909 = $272.7

Year 2 : $325 * 0.826 = $268.45

Year 3 : $360 * 0.751 = $270.36

Year 4 : $710 * 0.623 = $442.33

Now, we will calculate the cumulative present value (PV) of cash flows as per below:

Cumulative PV cash flows after year 1 = $272.7

Cumulative PV cash flows after year 2 = $272.7 + $268.45 = $541.15

Cumulative PV cash flows after year 3 = $272.7 + $268.45 + $270.36 = $811.51

Cumulative PV cash flows after year 4 = $272.7 + $268.45 + $270.36 + $442.33 = $1253.84

The cumulative PV cash flows reach the initial investment amount of $950 sometime in year 4.

Therefore the discounted payback period would be more than 3 years and less than 4 years. Steps in the calculation of payback period are given below:

a. Amount of cash flow in year 4 needed to reach $950 cumulative cash flows:

$950 - $811.51 (year 1's cumulative cash flow amount) = $138.49

b. Percentage of year 4 until cumulative amount of $950 is reached:

$138.49 / $442.33 = 0.313

c. Payback period = 3 + 0.313 = 3.313 years