Question

A- Martin is analyzing a project and has gathered the following data. Based on this data,

                       what is the average accounting rate of return? The firm depreciates it assets using

                       straight-line depreciation to a zero book value over the life of the asset.

                      

                                    Year                          Cash Flow             Net Income

                                       0                              -$642,000                       n/a

                                       1                              $170,000                $ 9,500

                                       2                              $240,000                $79,500

                                       3                              $205,000                $44,500

                                       4                              $195,000                $34,500

B- The Winston Co. is considering two mutually exclusive projects with the following cash flows:

                                                                        Project A               Project B

                                    Year                         Cash Flow             Cash Flow

                                       0                              -$75,000               -$60,000

                                       1                              $30,000                $25,000

                                       2                              $35,000                $30,000

                                       3                              $35,000                $25,000

           B-1 what is the IRR of project A?

           B-2 What is the IRR of project B?

           B-3 Based on the IRR rule, which project should be accepted and why?

           B-4 At what required rate of return will the company be indifferent between the two projects?

B-5 If Winston company has a required rate of return of 10%, which project (if any) should it accept and why?

B-6 If the company has a required rate of return of 15%, which project (if any) should it accept and why?

Answer 1

A-

Average accounting rate of return

= Average accounting profit/Average investment

= [($ 9,500 + 79,500 + 44,500 + 34,500)/4]/ [($ 642,000+$ 0)/2]

= ($ 168,000/4)/ ($642,000/2)

= $ 42,000/$ 321,000 = 0.130841121 or 13.08 %

B-

1.Computation of IRR using trial and error method:

Computation of NPV at discount rate of 15 %

Year	Cash Flow CA	Computation of PV Factor	PV Factor @ 15 % (F)	PV (CA x F)
0	-$75,000	1/(1+0.15)^0	1	-$75,000
1	30,000	1/(1+0.15)^1	0.86956521739130	26,086.95652
2	35,000	1/(1+0.15)^2	0.75614366729679	26,465.02836
3	35,000	1/(1+0.15)^3	0.65751623243199	23,013.06814
			NPV A1	$565.05302

As, NPV is positive, let’s compute NPV at discount rate of 16 %.

Year	Cash Flow CA	Computation of PV Factor	PV Factor @ 16 % (F)	PV (CA x F)
0	-$75,000	1/(1+0.16)^0	1	-$75,000
1	30,000	1/(1+0.16)^1	0.86206896551724	25,862.06897
2	35,000	1/(1+0.16)^2	0.74316290130797	26,010.70155
3	35,000	1/(1+0.16)^3	0.64065767354135	22,423.01857
			NPV A2	-$704.21091

IRR = R1 + [NPV A1 x (R2 – R1)/ (NPV A1 – NPV A2)]

= 15 % + [$ 565.05302 x (16% - 17%)/ ($ 565.05302 – (-$ 704.21091))]

= 15 % + [($ 565.05302 x 1 %)/ ($ 565.05302 +$ 704.21091)]

= 15 % + ($ 5.6505302/ $ 1,269.26392)

= 15 % + 0.004451817

= 15 % + 0.44 % = 15.44 %

IRR of the project A is 15.44 %

2-

1.Computation of IRR using trial and error method:

Computation of NPV at discount rate of 15 %

Year	Cash Flow CB	Computation of PV Factor	PV Factor @ 15 % (F)	PV (CB x F)
0	-$60,000	1/(1+0.15)^0	1	-$60,000
1	25,000	1/(1+0.15)^1	0.86956521739130	21,739.13043
2	30,000	1/(1+0.15)^2	0.75614366729679	22,684.31002
3	25,000	1/(1+0.15)^3	0.65751623243199	16,437.90581
			NPV B1	$861.34626

As, NPV is positive, let’s compute NPV at discount rate of 16 %.

Year	Cash Flow CB	Computation of PV Factor	PV Factor @ 16 % (F)	PV (CB x F)
0	-$60,000	1/(1+0.16)^0	1	-$60,000
1	25,000	1/(1+0.16)^1	0.86206896551724	21,551.72414
2	30,000	1/(1+0.16)^2	0.74316290130797	22,294.88704
3	25,000	1/(1+0.16)^3	0.64065767354135	16,016.44184
			NPV B2	-$136.94698

IRR = R1 + [NPV B1 x (R2 – R1)/ (NPV B1 – NPV B2)]

= 15 % + [$ 861.34626 x (16% - 15%)/ ($ 861.34626 – (-$ 136.94698))]

= 15 % + [($ 861.34626 x 1 %)/ ($ 861.34626 + $ 136.94698)]

= 15 % + ($ 8.6134626/ $ 998.29324)

= 15 % + 0.008628189

= 15 % + 0.86 % = 15.86 %

IRR of the project B is 15.86 %

3.

Based on IRR rule Project B should be accepted as it has higher IRR than Project A.