Question

Capital Budgeting For the following two projects, determine the 1. Payback Period 2. Discounted Payback 3. Net Present Value 4. Profitability Index (Benefit-Cost Ratio) 5. Internal Rate of Return 6. Modified Internal Rate of Return Project A Project B Year Net Income Cash Flow Net Income Cash Flow 0 (15,000) (19,000) 1 5,000 6,000 3,000 4,000 2 5,000 6,000 5,000 6,000 3 5000 6,000 7,000 8,000 4 5,000 6,000 11,000 12,000 Risk Index 1.80 .60 The firm’s cost of capital ko is 15% and the risk free rate Rf is 10%. The firm assesses risk and assigns a risk index to determine a risk adjusted discount rate. An index of 1.0 would be assigned to an average risk project. To determine risk adjusted rates the firm uses the following equation: Risk Adjusted Rate (RADR) = Rf + [Risk Index (ko – Rf) Task: Rank the projects in accordance with each method of analysis..

	Project A			Project B
Year		Net Income	Cash Flow		Net Income	Cash Flow
0			(15,000)			(19,000)
1		5,000	6,000		3,000	4,000
2		5,000	6,000		5,000	6,000
3		5000	6,000		7,000	8,000
4		5,000	6,000		11,000	12,000
Risk Index	1.80			.60

Answer 1

Project A :

Year	Cash Flow	Cummulative Cashflow	Discounting factor = 1/ ( 1+ r)^n	Present value	Cummulative present value
1	6000	6000	0.840336134	5042.016807	5042.016807
2	6000	12000	0.706164819	4236.988913	9279.00572
3	6000	18000	0.593415814	3560.494885	12839.5006
4	6000	24000	0.498668751	2992.012508	15831.51311
			Total	15831.51311

Risk adjusted rated for Project A = 10 + 1.8* ( 15 - 10) = 19%

Payback period = 2 + ( 15000-12000) / 6000 = 2.5 years

Discounted payback period = 3 + ( 15000 - 12839) / 2992.01 = 3.72 years

Net present value = present value of cash inflows - initial investment = 15831.51 - 15000 = 831.51

Profitability index = Present value of cash inflows / initial invetsmnet = 15831.51 / 15000 = 1.055

Project B :

Year	Cash Flow	Cummulative Cashflow	Discounting factor = 1/ ( 1+ r)^n	Present value	Cummulative present value
1	4000	4000	0.884955752	3539.823009	3539.823009
2	6000	10000	0.783146683	4698.8801	8238.703109
3	8000	18000	0.693050162	5544.401298	13783.10441
4	12000	30000	0.613318728	7359.824732	21142.92914
			Total	21142.92914

Payback period = 3 + ( 19000 - 18000) / 12000 = 3.08 years

Discounted payback period = 3 + ( 19000 - 13783) / 7359.82 = 3.71 years

Net present value = 21142.93 - 19000 = 2142.93

PI = 21142.93 / 19000 = 1.11