ABE TUTORIALS

PROBLEM 29: DETAILED IRR SOLUTION

A PROPOSED PROJECT REQUIRES AN INITIAL INVESTMENT OF P50,000. THE ESTIMATED YEAR-END REVENUES AND COSTS ARE TABULATED BELOW. AN ADDITIONAL INVESTMENT OF P25,000 IS REQUIRED AT THE END OF THE SECOND YEAR. THE PROJECT WILL TERMINATE AT THE END OF THE 5TH YEAR, WITH ASSETS ESTIMATED TO HAVE A SALVAGE VALUE OF P30,000. WHAT IS THE IRR FOR THIS PROJECT?

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Year	Revenue	Cost	Net Cash Flow
0	-	P50,000	-P50,000
1	P75,000	P60,000	P15,000
2	P90,000	P77,500 + P25,000	-P12,500
3	P100,000	P80,000	P20,000
4	P95,000	P75,000	P20,000
5	P60,000 + P30,000	P40,000	P50,000

a. 13%

b. 15%

c. 17%

d. 19%

Step-by-Step Analysis

1. Calculate Net Cash Flows (NCF) per Year:

• Year 0: -P50,000 (Initial Investment)
• Year 1: 75k - 60k = +P15,000
• Year 2: 90k - 77.5k - 25k (Additional Investment) = -P12,500
• Year 3: 100k - 80k = +P20,000
• Year 4: 95k - 75k = +P20,000
• Year 5: 60k - 40k + 30k (Salvage) = +P50,000

2. Manual Trial and Error (Interpolation):

We look for the rate where Present Worth of Inflows = Present Worth of Outflows.

Try i = 15%:
NPV = -50,000 + 15k(0.8696) - 12.5k(0.7561) + 20k(0.6575) + 20k(0.5718) + 50k(0.4972)
NPV = +P3,036 (Too low, IRR is higher)

Try i = 17%:
NPV = -50,000 + 15k(0.8547) - 12.5k(0.7305) + 20k(0.6244) + 20k(0.5337) + 50k(0.4561)
NPV = -P345 (Too high, IRR is lower)

3. Final Interpolation:

IRR = 15% + [ (17% - 15%) × (3036 - 0) / (3036 - (-345)) ]
IRR = 15% + [ 2% × (3036 / 3381) ]
IRR = 15% + 1.79% = 16.79%

The closest answer is Choice C (17%).