Appendix 10A
Mutually Exclusive Investments Having Unequal Lives
APPENDIX 10A
MUTUALLY EXCLUSIVE INVESTMENTS
HAVING UNEQUAL LIVES
SOLUTIONS TO PROBLEMS:
1. a. NPVA = -$30,000 + $10,500(3.037) = $1,888.50
b. NPVA(chain) = $1,888.50 – $30,000(PVIF.12,4 )
c. Alternative A should be chosen because it has the higher positive
d. NPVA = $1,888.50 (from part a)
Equivalent annual annuity (A) = $1,888.5/3.037 = $621.83
The equivalent annual annuity method also recommends project A.
2. NPVP = – $100,000 + $22,000 (PVIFA0.12,10)
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Appendix 10A
Mutually Exclusive Investments Having Unequal Lives
NPVR = – $85,000 + $18,000 (PVIFA0.12,8)
Equivalent annual annuity (P) = $24,300/(PVIFA0.12,10)
Equivalent annual annuity (R) = $4,424/(PVIFA0.12,8)
NPVP (assuming in1nite replacement)
NPVR (assuming in1nite replacement)
Investment P should be selected, because it has the higher net present
value when evaluated over an in1nite replacement horizon.
3. NPVA = – $50,000 + $25,000 (PVIFA0.19,3)
NPVB = – $79,000 + $28,000 (PVIFA0.19,5)
Equivalent annual annuity (A) = $3,500/(PVIFA0.19,3)
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Appendix 10A
Mutually Exclusive Investments Having Unequal Lives
Equivalent annual annuity (B) = $6,624/(PVIFA0.19,5)
NPVA (assuming in1nite replacement)
NPVB (assuming in1nite replacement)
Investment B should be selected, because it has the higher net present
value when evaluated over an in1nite replacement horizon.
4. a. NPVD = -$50,000 + $24,000(2.322) = $5,728
b. NPVD (replacement chain) = $5,728 – $50,000 (PVIF0.14, 3)
b. Investment D should be chosen because it has the higher positive
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Appendix 10A
Mutually Exclusive Investments Having Unequal Lives
Investment D should be selected because it has the higher net
present value when evaluated over an in1nite replacement
horizon.
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