Question

4(a) Expected cash flows for a strip-mining project are estimated as shown below. 7 8 End of 0 year Cash -100,000 flow 20,000 100.000 100.000 50,000 50,000 50,000 50,000 -350,000 A startup cost is incurred immediately. The income exceeds outlays for the next 7 years. During the 8th year, the major cost is for landscape improvement. Does the strip mining project appear to be a profitable investment? On the basis of past experience, the mining company wishes to use MARR of 40%. Also, the company is keen on finding out the internal rate-of-return (i.e. IRR). NOTE: Check for dual rates of return. 4(b) You have an opportunity to buy a bond with a face value of $10,000 and coupon rate of 14%, payable semi-annually. NOTE: Interest per 6-month period is 7% of Face Value (ie. $10,000x0.07 = $700 per 6-month period). (i) If the bond matures in five years and you can currently buy one for $8,000, what is your IRR for this investment? (ii) If your MARR for this type of investment is 20%, should you buy the bond?

Answer 1

4(a)

NPV calculation:

P10 AB 1 MARR 40% C D E F G H 2 1 3 End of year 4 Cash flow 2 4 $20,000 $100,000 $100,000 $50,000 5 $50,000 ($100,000) $50,000 $50,000 ($350,000) 5 6 NPV $ 11,729.02

Formulas used are as follows:

B6 fc =B4+NPV(B1,04:14) B c А o E F G H I 1 MARR 10.4 3 End of year 4 Cash flow 4 50000 5 5 50000 6 50000 7 50000 8 -350000 |-100000 120000 100000 100000 5 6 NPV 7 =B4+NPV(B1,C4:14)

As the NPV is positive, the strip mining project appears to be a profitable investment.

IRR calculation:

The project has two cash outflows, first in year 0 and then in year 8. In such cases, it is likely that there will be two IRR's due to on-conventional cash flow pattern. Therefore, to calculate the two IRR, we can calculate NPV's at different discount rates and check at which discount rates the NPV is zero. We can plot the same in a graph.

34 5 $20,000 $100,000 $100,000 $50,000 $50,000 ($100,000) $50,000 $50,000 ($350,000) 3 End of year 4 Cash flow 5 6 NPV $11,729 NPV 6% 8 Discount rates (NPV 0% ($30,000) $17,704 12% $35,492 18% $38,380 24% $34,047 30% $26,466 36% $17,694 42% $8,782 48% $245 54% ($7,686) $50,000 $40,000 $30,000 $20,000 $10,000 $0 ($10,000) n , 0% ($20,000) ($30,000) ($ 40,000) NPV i 10% 20% 30% 40% 50% 60%

We can also calculate the IRR's using different guess rates in IRR function.

N15 C D G H 1 MARR 40% 3 End of year 4 Cash flow ($100,000) $20,000 $100,000 $100,000 $50,000 5 $50,000 6 $50,000 $50,000 $350,000) 5 $11,729 IRR 6 NPV 7 8 Guess rate 5% 10% 15% 3.13% 3.13% 3.13% 48.18% 48.18% 48.18% 20% 25% 30%

Formulas used:

B9 - fc =IRR($B$4:$J$4,49) А 0.4 1 MARR 2 3 End of year 4 Cash flow 1 20000 100 80000 50000 30000 I-100000 350000 100000 100000 50000 50000 50000 50000 -350000 =B4+NPV(B1,C4:14) 6 NPV 7 8 Guess rate 9 0.05 10 0.1 11 0.15 12 0.2 13 0.25 14 0.3 IRR J=IRR($B$4:$J$4,491 =IRR($B$4:$J$4, A10) =IRR($B$4:$J$4,A11) =IRR($B$4:$J$4, A12) =IRR($B$4:$J$4, A13) =IRR($B$4:$J$4,414)

So, the IRR rates are 3.13% and 48.18%.