Question

Al Bundy wants to start a shoe store. It will cost $150,000 to get the business started. Al can borrow the money from a bank at 5.5% interest rate. The estimated net cash flows from the business for the first 6 years are:    -$50,000; -$20,000; $100,000; $180,000; $300,000; $360,000. Al will be happy to earn at least 12% so use a 12% discount rate. Answers questions 21-23.

21. The net present value of this business opportunity is:

   a. $327,600                c. $387,600

   b. $487,600                d. None

22. The internal rate of return of this business opportunity is:

   a. 33.32%            c. 19.90%

   b. 38.48%            d. None

23. How much is the payback period for this business opportunity?

   a. 6.5 Years         c. 3.75 Years

   b. 7.5 Years         d. None

Answer 1

Question 21: Net present Value

Net present value = Discounted cash inflows - Discounted cash outflows

Year	Cash Flow	Present value factor @12%	Discounted Cash Flow
0	(150000)	1	(150000)
1	(50000)	0.893	(44643)
2	(20000)	0.797	(15944)
3	100000	0.712	71178
4	180000	0.635	114393
5	300000	0.567	170228
6	360000	0.507	182387

Discounted Cash inflows = 71178 + 114393 + 170228 + 182387 = $538186

Discounted Cash Outflows = 150000 + 44643 + 15944 = $210586

So Net present value = $538186 - $210586 = $327600

So the Answer is Option A.

Question 22:

Internal rate of return is the rate at which Net present value is equal to Zero.

Internal rate of return(IRR) can be calculated for a multiple uneven cash flow using Guess rate method.

Let us assume the IRR is 36%

Year	Cash Flow	Present value factor @36%	Discounted Cash Flow
0	(150000)	1	(150000)
1	(50000)	0.735	(36765)
2	(20000)	0.541	(10813)
3	100000	0.397	39754
4	180000	0.292	52616
5	300000	0.215	64480
6	360000	0.158	56894

Discounted Cash inflow = $213745

Discounted cash outflow = $197578

Net present value = 213745 - 197578 = $16167

Let the guess rate be 40%. Then NPV will be as follows:

Year	Cash Flow	Present value factor @40%	Discounted Cash Flow
0	(150000)	1	(150000)
1	(50000)	0.714	(35714)
2	(20000)	0.510	(10204)
3	100000	0.364	36443
4	180000	0.260	46855
5	300000	0.186	55780
6	360000	0.133	47812

Discounted Cash inflow = $186891

Discounted cash outflow = $195918

Net present value = 213745 - 197578 = - $9027

At 36% , NPV = 16167

At 40%, NPV = -9027

For every 1% increase in IRR, NPV reduces by (16167+9027) / 4 = 6300.

The NPV should reduce from 16167 to 0. So it should get reduced by $16167.

1% --------6300

x %---------16167

x = 16167 / 6300 = 2.48 approximately

So the IRR should increase by 2.48% from 36% to make NPV = 0

So the internal rate of return = 38.48%

So the Answer is Option B.

Question 23: Pay Back period

Year	Unrecovered Investment at the start of year	Investment required	Cash Inflow	Unrecovered investment at the end of year
0	0	150000	0	150000
1	150000	50000	0	200000
2	200000	20000	0	220000
3	220000	0	100000	120000
4	120000	0	180000	0

Pay back period = (Years before full recovery) + (Unrecovered investment at the start of year / Cash flow during the year)

Pay back period = 3 + (120000/180000) = 3.67 years approximately 3.75 years.

So the answer is Option C.