Question

Brett Collins is reviewing his company's investment in a cement plant. The company paid $14,800,000 five years ago to acquire the plant. Now top management is considering an opportunity to sell it. The president wants to know whether the plant has met original expectations before he decides its fate. The company's discount rate for present value computations is 9 percent. Expected and actual cash flows follow: (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.) Expected Actual Year 1 $3,380,000 2,640,000 Year 2 $5,010,000 3,040,000 Year 3 $4,570,000 4,870,000 Year 4 $5,050,000 3,870,000 Year 5 $4,250,000 3,530,000 Required a.&b. Compute the net present value of the expected and actual cash flows as of the beginning of the investment. (Negative amounts should be indicated by a minus sign. Round your intermediate calculations and final answer to the nearest whole dollar.) a. Net present value (expected) b. Net present value (actual)

Answer 1

Ans. 1(a)

Year	Expected Cash Flow	PV Factor	Present Value
0	-14800000	1.00	-14800000
1	3380000	0.92	3100917.43
2	5010000	0.84	4216816.77
3	4570000	0.77	3528878.50
4	5050000	0.71	3577547.32
5	4250000	0.65	2762208.39
	Present Value (Expected)		2386368.41

Ans. 1(b)

Year	Actual Cash Flow	PV Factor	Present Value
0	-14800000	1.00	-14800000
1	2640000	0.92	2422018.35
2	3040000	0.84	2558707.18
3	4870000	0.77	3760533.55
4	3870000	0.71	2741605.57
5	3530000	0.65	2294257.79
	Present Value (Actual)		-1022877.56

Ans. 2(a)

Year	Cash Flow (A)	PV Factor	Present Value
0	-117000	1.00	-117000
1	46221	0.94	43604.72
2	46221	0.89	41136.53
3	46221	0.84	38808.04
	Net Present Value (A)		6549.29

Year	Cash Flow (B)	PV Factor	Present Value
0	-41000	1.00	-41000
1	17660	0.94	16660.38
2	17660	0.89	15717.34
3	17660	0.84	14827.68
	Net Present Value (B)		6205.39

Based on Net Present Value, project A should be selected.

Ans. 2(b)

IRR is that discount rate at which NPV is zero. To calculate approximate IRR(r), let us use hit and trial method:

Project A

Let r = 8%

Then NPV is as follows:

Year	Cash Flow (A)	PV Factor	Present Value
0	-117000	1.00	-117000
1	46221	0.93	42797.22
2	46221	0.86	39627.06
3	46221	0.79	36691.72
	Net Present Value (A)		2116.00

Since NPV is not equal to zero, let us try r = 9%

For r = 9%, NPV is as follows:

Year	Cash Flow (A)	PV Factor	Present Value
0	-117000	1.00	-117000
1	46221	0.92	42404.59
2	46221	0.84	38903.29
3	46221	0.77	35691.09
	Net Present Value (A)		-1.03

Since NPV approximately equals to zero, IRR of project A is 9%.

Project B

Let r = 12%

Then NPV is as follows:

Year	Cash Flow (B)	PV Factor	Present Value
0	-41000	1.00	-41000
1	17660	0.89	15767.86
2	17660	0.80	14078.44
3	17660	0.71	12570.04
	Net Present Value (B)		1416.34

Since NPV is not equal to zero, let us try r = 14%

For r = 14%, NPV is as follows:

Year	Cash Flow (B)	PV Factor	Present Value
0	-41000	1.00	-41000
1	17660	0.88	15491.23
2	17660	0.77	13588.80
3	17660	0.67	11920.00
	Net Present Value (B)		0.02

Since NPV approximately equals to zero, IRR of project B is 14%.

Since 14%>9%, Project B is chosen based on IRR.

Ans. 3(a-1)

Calculation of Unadjusted rate of return:
Increase in Future Net Income	6200
Initial Investment	107000
Unadjusted rate of return	=Increase in net income/Initial Investment
	=6200/107000
	5.79%

Ans. 3(a-2)

Since the unadjusted rate of return of 5.79% is less than the minimum required rate of return of 10%, the company should not invest in the equipment.

Ans. 3(b-1)

Let us now calculate IRR of the project.

Let IRR(r) be 12%.

Year	Cash Flow (A)	PV Factor	Present Value
0	-107000	1.00	-107000
1	29683	0.89	26502.68
2	29683	0.80	23663.11
3	29683	0.71	21127.77
4	29683	0.64	18864.08
5	29683	0.57	16842.93
	Net Present Value (A)		0.57

Since NPV at IRR 12% is approximately equals to zero, IRR is 12%.

Ans. 3(b-2)

Based on IRR the company should invest in the project as IRR 12% is greater than minimum required rate of return of 10%.

Ans. 3(c)

IRR is a better method than unadjusted rate of return since IRR considers time value of money and is also based on future cash flows which gives better picture.