Question

Supppose a firm has decided to invest in a project which has the following cash flow structure. The project has annual costs of $10 starting today and growing by 3% each subsequent year. The project also generates revenues of X starting 10 years from today, and these cash flows grow by 2% each year after that. Both revenue and costs are perpetuities.

a. Suppose X=$30 and the discount rate is 6%.

i. What is the NPV of the project? (Note NPV is positive)

ii. Qualitatively, what happens to project cash flows far into the future?

iii. Is the IRR unique? Briefly explain why. (Hint: you don't need to calculate the IRR).

b. Suppose now that X=$11 and the discount rate is 6%.

i. Note that in year 10, profits are negative. Does the IRR exist? Briefly explain why. (again, you don't need to calculate the IRR.)

c. Suppose again that X=$30 and the discount rate is 6%. In addition, asssume the firm has the option to abandon the project at a one-time coost of $80 at any future date of its choosing. What is the NPV of the project that has this abandoment option?

Answer 1

Imp Points

1. Cost is $10 today and annually growing by 3%
2. Revenue is X starting 10 years from today with annual growth of 2%
3. Which means cost will occur today and revenue will occur after 10 year.
4. Both are perpetual

Ans a) Suppose X=$30 and the discount rate is 6%.

i. What is the NPV of the project? (Note NPV is positive)

Ans - 187.83 kindly refer table below for detail

	0	1	2	3	4	5	6	7	8	9	10
Cost with 3% annual growth	10	10.3	10.609	10.92727	11.25509	11.59274	11.94052	12.29874	12.6677	13.04773	13.43916
Revenue with 2% annual growth											30
Net Inflows	-10	-10.3	-10.609	-10.9273	-11.2551	-11.5927	-11.9405	-12.2987	-12.6677	-13.0477	16.56084
Discount Rate @ 6%	-10	-9.7169811	-9.44197	-9.17475	-8.91508	-8.66277	-8.4176	-8.17936	-7.94787	-7.72293
Year 10 with perpetual growth											276.0139
NPV Sum of all the flows	187.83462

ii. Qualitatively, what happens to project cash flows far into the future?

Ans ) As growth rate of cost is more than the growth rate of revenue so far into the future Cashflow will turned out negative.

iii. Is the IRR unique? Briefly explain why. (Hint: you don't need to calculate the IRR).

Ans ) As explained in above that far into the future Cashflow will turned out negative. SO this is the case of sign change cashflow with both positive and negative sign in between so projects have dual IRR so IRR is not unique.

b. Suppose now that X=$11 and the discount rate is 6%.

i. Note that in year 10, profits are negative. Does the IRR exist? Briefly explain why. (again, you don't need to calculate the IRR.)

Ans ) Yes with X being 11 in 10th year Cost is higher than profit and cashflow is negative by 2.43916 so we won't be able to calculate IRR as all the years are with only negative inflows. Where IRR is a point where Present Value of Cash Inflows and Cash Outflows are Zero . In this case there is no inflows.

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