Question

1. Capital Budgeting: . To or Co is $25,000 r=10% N 1 Cash Flows $5,000 $8,000 $13,000 $10,000 3 4

Don't use excel

Answer 1

Given:

Capital outlay (CO): $25,000

Rate r: 10%

Cash inflows:

Year	Amount ($)
1	5,000.00
2	8,000.00
3	13,000.00
4	10,000.00

Let's start with the calculation of NPV first.

NPV = Present value of cash inflows - Capital outlay ----------- (1)

Year	Amount ($)	Discounting Factor	Present value of cash flows ($)
0	(25,000.00)	-	(25,000.00)
1	5,000.00	1.1	4,545.45
2	8,000.00	1.12	6,611.57
3	13,000.00	1.13	9,767.09
4	10,000.00	1.14	6,830.13
NPV			2,754.25

Payback period (PP)

Payback period = Full years until recovery of CO + Unrecovered cash at the beginning of the recovery year / Cash inflow during the recovery year ------------- (2)

Year	Amount ($)	Cumulative Cashflow ($)
0	(25,000.00)	(25,000.00)
1	5,000.00	(20,000.00)
2	8,000.00	(12,000.00)
3	13,000.00	1,000.00
4	10,000.00	11,000.00

From the above table, we see that the cumulative cash flows turn positive in the third year, which is the recovery year.

So substituting the values in formula (2), we get

PP = 2 + 12,0000/13,000 = 2.92 years

It takes 2.92 yrs to recover the initial cash outlay of $25,000

Discounted Payback period (DPP)

Payback period = Full years until recovery of CO + Unrecovered cash at the beginning of the recovery year / Discounted cash inflow during the recovery year ------------- (3)

Year	Amount ($)	Discounted cash flows (DCF) ($)	Cumulative DCF ($)
0	(25,000.00)	(25,000.00)	(25,000.00)
1	5,000.00	4,545.45	(20,454.55)
2	8,000.00	6,611.57	(13,842.98)
3	13,000.00	9,767.09	(4,075.88)
4	10,000.00	6,830.13	2,754.25

In the above table, the discounted cash flows are the ones we used for calculating the NPV. We see that the cumulative cash flows turn positive in the fourth year, which is the recovery year.

So substituting the values in the formula, we get

DPP = 2 + 4,075.88 / 6,830.13 = 3.60 years

It takes 3.6 yrs to recover the initial outlay at discounted cash flows.

Profitability Index

Profitability index = Present value of cash inflows / Capital Outlay = 27,754.25 / 25,000 = 1.11

Internal Rate of Return

Internal rate of return for this project can be calculated as follows:

--------------- (4)

CFI CF2 CF3 CF4 (1 + IRR)*(1 + IRR)2 *(1 + IRR)*(1 + IRR)4

where,

CF1, CF2, CF3 and CF4 represent cash inflows years 1, 2, 3 and 4 respectively

IRR is the internal rate of return

Now, if we are not using Excel, we can solve this equation for IRR using trial and error method, i.e., we substitute an approximate value for IRR in (4) and adjust from there.

In the NPV calculation, we found that at 10% discount rate, the NPV is positive. So the IRR has to be greater than 10% to satisfy (4). So let's start with 12%.

(5,000 / 1.12) + (8,000 / 1.12²) + (13,000 / 1.12³) + (10,000 / 1.12⁴) - 25,000 = 1,450.16 which is greater than 0.

Let's increase the IRR to 14%

(5,000 / 1.14) + (8,000 / 1.14²) + (13,000 / 1.14³) + (10,000 / 1.14⁴) - 25,000 = 237.14 which is still greater than 0 but closer to it.

If we assume an IRR of 15%

(5,000 / 1.15) + (8,000 / 1.15²) + (13,000 / 1.15³) + (10,000 / 1.15⁴) - 25,000 = -337.78 which is less than 0.

Now, using interpolation, we find that the IRR is close to 14.4%.

From the calculation of above project parameters, we find that the profitability index is greater than 1, indicating that the PV of the cash inflows is greater than the capital outlay. The investment returns an NPV of $2,754.25 at the end of four years. So the project can be accepted. Further, the projects IRR of 14.4% also has to be greater than the opportunity cost of capital.