Question

The Panhandle Corporation is considering whether to go ahead with a small-scale trial project that requires an initial outlay of $900,000 and, if successful produce cash inflows of $450,000 in year one followed by $540,000 per year in perpetuity starting at the end of year two. If not successful, the project will produce no cash flows. The probability of success is 38%. Given the extreme riskiness of this project the company decides to use 28% as a risk-adjusted discount rate for this project.

a. Given the above information and based on static analysis, should the company go ahead with its investment?

b. Upon further study the company realizes that, if the project was successful, it creates an opportunity to expand production by investing an additional $9 million at the end of year one. The new investment would increase the project cash flows to $2.20 million (instead of $540,000) per year in perpetuity. Also, at that point the company feels that a major part of the risk associated with the project would have been resolved and that from year one on it can use its WACC of 15%. Given this information, should the company go ahead with the investment?

c. What is the present value of the option to expand?

Answer 1

Answer>

From the decision tree method of analysis:

NPV = Net Present Value = Present value of all cash inflow - Present value of all cash outflow

We will undertake the project only if NPV > 0

Since there is a probablity of project failure, we will use decision tree analysis to find the total present value of cash inflows

PV of cash inflow = (Probablity of success * PV of cash flows in case of success) + (Probablity of failure * PV of cash inflow in case of failure)

Here,

PV of cash inflow in case of failure = 0 (since there will be no cash outout in case of failure)

Hence,

PV of cash inflow = (Probablity of success * PV of cash flows in case of success) + (Probablity of failure * 0)

PV of cash inflow = (Probablity of success * PV of cash flows in case of success)

PV of cashflow = CF/(1+r)^n,

Where

CF = cashflow at year n

r = discount rate = WACC

n = year

PV of cashflows in perpertuity from year 2

= (CF/(1+r)^2)/(1-(1/(1+r))) (since PV of cash flows will be in infinite gp series with first term as PV of year 2 and common ratio as 1/(1+r))

=(CF/(1+r)^2)/(1-(1/(1+r)))

=(CF/(1+r)^2)/((1+r-1)/(1+r)))

=CF/(1+r)*(r)

a> Let's analyse the first scenario

r = 28%

Total cash outflow (Year 0) = 900000 = Present Value

Cash inflow in first year = 450000

PV of 1st year cash inflow = 450000 / (1+0.28)

CF1 = 450000/1.28 = 351562.5

Cash inflow from second year onwards = 540000

Perpetual cash flow = 540000

Sum of perpetual cash inflows = 540000 /(1+0.28)*(0.28)

=540000/(1.28*0.28)

=1506696.43

Total PV of cash inflows = PV of Cash inflow at year 1 + PV of perpetual cash inflows

Total PV of cash inflows = 351562.5 + 1506696.43 = 1858258.93

Hence present value of cash inflows if project successful = 0.38 * 1858258.93 = 706138.39

Net Present Value = PV of cash inflows - PV of cash outflows

NPV = 706138.39 - 900000 = -193861.61

Since the NPV is negative, hence the company should not go ahead with this investment

b> Let's analyse the second scenario

r = 15%

Total cash outflow (Year 0) = 900000 = Present Value

Cash outflow (Year 1) = 9000000

PV = 9000000/(1+0.15) = 7826086.96

Total PV of cash outflows = 7826086.96 + 900000 = 8726086.96

Cash inflow in first year = 450000

PV of 1st year cash inflow = 450000 / (1+0.15)

CF1 = 450000/1.15 = 391304.35

Cash inflow from second year onwards = 2200000

Perpetual cash flow = 2200000

Sum of perpetual cash inflows = 2200000 /(1+0.15)*(0.15)

=2200000/(1.15*0.15)

=12753623.19

Total PV of cash inflows = PV of Cash inflow at year 1 + PV of perpetual cash inflows

Total PV of cash inflows = 391304.35 + 12753623.19 = 13144927.54

Hence present value of cash inflows if project successful = 0.38 * 13144927.54 = 4995072.46

Net Present Value = PV of cash inflows - PV of cash outflows

NPV = 4995072.46 - 8726086.96 = -3731014.49

Since the NPV is negative, hence the company should not go ahead with this investment as well

c>

Present value of the option to expand =

Total PV of cash inflows = 391304.35 + 12753623.19 = 13144927.54 (from a)

Total PV of cash inflows previously = 1858258.93 (from b)

Total PV of option to expand = PV of cash new inflows - PV of old Cash inflow

= 13144927.54 - 1858258.93 = 11286668.61

Hope this answers your question