Question

(NEED 5&6 PLEASE) You are considering the purchase of a small Youth Hostel in the ski country of Northern Idaho, USA. The initial cost of this purchase is $125,000. The after-tax cash flow from this investment is estimated to be $30,000 per year for the next 5 years. The opportunity cost of capital is 8%. Calculate the following. Initial cost = $125,000 After tax cash flow= $3,000 per years for 5 years Cost of Capital = 8% 1. The Payback Period – should you buy the youth hostel if your required payback is less than 4 years? Pay back period = Initial investment/After tax cash flow each year =125,000/3,000 = 4.17 years approx.. If required payback is less than 4 years then this hostel should not be bought. 2. The present value of the benefits (PVB) PVB= Annual cash flow x PVAF (8%,5) =3,000 x PVAF (8%,5) =$11,97.81 .30 3. The present value of the costs (PVC) PV of costs = Initial investment because this is the only one cost which is at year 0, this PV of costs = $125,000 4. The net present value (NPV) – should you buy the youth hostel based on NPV rules? NPV=IV of annual cash inflows -Initial Investment =11,971.30 – 125,000 =-$5218.70 NPV is negative so the hostel should not be bought. 5. Profitability Index (PI) – what does the profitability index mean in terms of buying the youth hostel? 6. Internal Rate of Return (IRR) (use interpolation) – should you buy the youth hostel based on IRR rules?

Answer 1

As a solution to 5 and 6 is required,

5) Profitability Index (PI) = Present value of future cash flow / Initial Investment in the project.

Now Present Value of future cash flow is as follows :

​

So calculating present value for 30000 which will be received for five years. r, in this case, will be the opportunity cost of capital.

No of year	Future Value	1+r	(1+r)^n	Present Value
1	30000	1.08	1.08	27777.78
2	30000	1.08	1.17	25720.16
3	30000	1.08	1.26	23814.97
4	30000	1.08	1.36	22050.90
5	30000	1.08	1.47	20417.50

Profitability Index (PI) = Present value of future cash flow / Initial Investment in the project.

=( 27777.78+25720.16+23814.97 + 22050.90+ 20417.50)/ 125000

= 0.96

6) Internal rate of return is as follows :

Internal Rate of Return  =  R1  +	NPV1 x (R2 - R1)
	(NPV1 - NPV2)

Where:

R1      =   Lower discount rate

R2      =   Higher discount rate

NPV1   =   Higher Net Present Value (derived from R1)

NPV2   =   Lower Net Present Value (derived from R2)

Let us assume two discount rates R1 = 10% and R2 = 20% . Now let us calculate net present value using these two discount rates .

Result for R1 =10%

No of year	Future Value	1+r	(1+r)^n	Present Value
0	-125000.00			-125000.00
1	30000.00	1.10	1.10	27272.73
2	30000.00	1.10	1.21	24793.39
3	30000.00	1.10	1.33	22539.44
4	30000.00	1.10	1.46	20490.40
5	30000.00	1.10	1.61	18627.64
			Total	-11276.40

Result for R2= 20%

No of year	Future Value	1+r	(1+r)^n	Present Value
0	-125000.00			-125000.00
1	30000.00	1.20	1.20	25000.00
2	30000.00	1.20	1.44	20833.33
3	30000.00	1.20	1.73	17361.11
4	30000.00	1.20	2.07	14467.59
5	30000.00	1.20	2.49	12056.33
			Total	-35281.64

Internal Rate of return =

=  R1%  +	NPV1 x (R2 - R1)%
	(NPV1 - NPV2)

= 10% + (-11276.40 * (20-10)%) / (-11276.40 - (-35281.64) = 10% + (-11276.40*10%) / 24005.24

= 10% - 4.7%= 5.3%

As per IRR rule , investment should only be selected where the cost of capital is less than IRR. In our case cost of capital is 8% which is higher than IRR, hence investment should not be made in youth hostel.