Question

a firm must choose between two mutually exclusive projects, a & b. project a has an initial cost of $10000. its projected net cash flows are $800, $2000, $3000, $4000, and $5000 at the end of years 1 through 5, respectively. project b has an initial cost of $14000, and its projected net cash flows are $7000, $5000, $3000, $2000, and $1000 at the end of years 1 through 5, respectively. the firm’s cost of capital is 6.00%. choose the correct statement:

A the npv and the irr criteria provide the same ranking of these two projects.

B the npv criterion recommends project a while the irr criterion recommends project b.

C the npv criterion recommends project b while the irr criterion recommends project a.

D the npv and irr criteria provide different rankings, but suggest that both projects should be taken.

E the npv and irr criteria provide the same ranking, but suggest that both projects should be taken.

Answer 1

The calculations for project A are shown below:

Year	Cash flow (CF)	Present value Factor @ 6%(Pv)	CF*Pv
0	-10000	1	-10000
1	800	0.943396226	754.7169811
2	2000	0.88999644	1779.99288
3	3000	0.839619283	2518.857849
4	4000	0.792093663	3168.374653
5	5000	0.747258173	3736.290864
NPV =	1958.233228
IRR=	11.44%

NPV= 1958.233228

let the IRR be r

The IRR is the rate at which NPV is zero

so, 10000 = 800/(1+r) + 2000/(1+r)^2 + 3000/ (1+r)^3 + 4000/ (1+r)^4 + 5000/(1+r)^5

Solving for r by trial and error method or excel, r = 0.1144 or 11.44%

The calculations for project B are shown below:

Year	Cash flow (CF)	Present value Factor (Pv) @ 6%	CF*Pv
0	-14000	1	-14000
1	7000	0.943396226	6603.773585
2	5000	0.88999644	4449.9822
3	3000	0.839619283	2518.857849
4	2000	0.792093663	1584.187326
5	1000	0.747258173	747.2581729
NPV =	1904.059133
IRR=	12.83%

NPV= 1904.059133

let the IRR be r

The IRR is the rate at which NPV is zero

so, 14000 = 7000/(1+r) + 5000/(1+r)^2 + 3000/ (1+r)^3 + 2000/ (1+r)^4 + 1000/(1+r)^5

Solving for r by trial and error method or excel, r = 0.1283 or 12.83%

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So we see NPV of A and IRR of B is higher

Hence, the correct option is

B) the npv criterion recommends project a while the irr criterion recommends project b.