Question

Question 1 : Company has 4 revenue options.
Option A: initial cost of $300,000, annual savings of $65,000, salvage of $150,000, useful life of 6 years
Option B: initial cost of $495,000, annual savings of $80,000, an additional one-time saving of $150,000 in year 3, salvage of $250,000, useful life of 4 years
Option C: initial cost of $350,000, annual savings of $100,000, salvage of $200,000, useful life of 3 years
Option D: initial cost of $400,000, annual savings of $100,000, salvage of $300,000, useful life of 2 years
a) If the options are independent and MARR is 15%, which should be selected? Justify answer using ROR.
b) If the options are mutually exclusive and MARR is 15%, which should be selected? Just answer using ROR.
c) If MARR is 20%, which should be selected if they are independent options?
d) If MARR is 20%, which should be selected if they are mutually exclusive?

Answer 1

NPV = Present value of cash inflows - Initial cost

Only options with a positive NPV should be selected in case of independent options.

In case of mutually exclusive options, the one with the highest positive NPV should be selected.

a) 15% rate and Independent options

Option A

NPV = [ $65,000 x PVIFA (15%, 6 years) + $150,000 x PVIF (15%, 6th year) ] - $300,000

or, NPV = [ $65,000 x 3.78448269385 + $150,000 x 0.43232759589 ] - $300,000 = $10,840.51

Option B

NPV = [ $80,000 x PVIFA (15%, 4 years) + $150,000 x PVIF (15%, 3rd year) + $250,000 x PVIFA (15%, 4th year) ] - $495,000

or, NPV = [ $80,000 x 2.85497836268 + $150,000 x 0.65751623242 + $250,000 x 0.57175324558 ] - $495,000 = (-)$25,035.98

Option C

NPV = [ $100,000 x PVIFA (15%, 3 years) + $200,000 x PVIF (15%, 3rd year) ] - $350,000

or, NPV = [ $100,000 x 2.2832251171 + $200,000 x 0.65751623242 ] - $350,000 = $9,825.76

Option D

NPV = [ $100,000 x PVIFA (15%, 2 years) + $300,000 x PVIF (15%, 2nd year) ] - $400,000

or, NPV = [ $100,000 x 1.62570888468 + $300,000 x 0.75614366729 ] - $400,000 = (-)$10,586.01

In case these are independent options, then Option A and option C should be selected as they have positive NPVs.

b) 15% rate and mutually exclusive options

In case these are mutually exclusive options, then Option A should be selected since it has the highest positive NPV.

c) 20% rate and independent options

Option A

NPV = [ $65,000 x PVIFA (20%, 6 years) + $150,000 x PVIF (20%, 6th year) ] - $300,000

or, NPV = [ $65,000 x 3.32551011654 + $150,000 x 0.33489797666 ] - $300,000 = (-)$33,607.15

Option B

NPV = [ $80,000 x PVIFA (20%, 4 years) + $150,000 x PVIF (20%, 3rd year) + $250,000 x PVIFA (20%, 4th year) ] - $495,000

or, NPV = [ $80,000 x 2.58873456788 + $150,000 x 0.5787037037 + $250,000 x 0.48225308641 ] - $495,000 = (-)$80,532.41

Option C

NPV = [ $100,000 x PVIFA (20%, 3 years) + $200,000 x PVIF (20%, 3rd year) ] - $350,000

or, NPV = [ $100,000 x 2.10648148147 + $200,000 x 0.5787037037 ] - $350,000 = (-)23,611.11

Option D

NPV = [ $100,000 x PVIFA (20%, 2 years) + $300,000 x PVIF (20%, 2nd year) ] - $400,000

or, NPV = [ $100,000 x 1.5277777777 + $300,000 x 0.69444444444 ] - $400,000 = (-)$38,888.89

Since all the options have negative NPV @20%, none of the options should be accepted.

d) None of the options should be accepted since they all have negative NPVs.

NOTE : PVIF = present value interest factor of $1 = 1 / (1 + r)ⁿ

for example, @20% for 2nd year, PVIF = 1 / (1 + 0.20)² = 0.69444444444

PVIFA = present value interest factor annuity of $1 =

for example, @20% for 2 years, PVIFA =