Question

NPC is considering either to invest in a project for a new product immediately or 1 year later. If NPC invests in the project today, there will be 75% chance of good market acceptance of the product and 25% chance of bad market acceptance of the product. If market reaction to the new product is good, a cash inflow of $500 million will be realized each year for the next 7 years. If market reaction to the new product is bad, a cash inflow of $25 million will be realized each year for the next 7 years. However, if NPC chooses to wait for 1 year to obtain more information about market tastes, the company would know definitely about the market reaction and would then either proceed with the project or not invest in it at all. The initial cost of the project is $1,500 million.

1. Assuming that all cash flows are discounted at 10%, if NPC chooses to wait a year before proceeding and the project will still end 7 years from now, how much will this increase or decrease the project's expected NPV in today's dollars (i.e., at t = 0), relative to the NPV if it proceeds today?
2. Using the same data, estimate the effect of waiting on the project's risk i.e. calculate by how much the one-year delay will reduce the project's coefficient of variation. (Hint: Use the expected NPV.)

Please show your work on Excel with calculations and formulas.

Answer 1

a)

Year	Cashflow	Present value Cashflow (Good market)	Cashflow	Present Value Cashflow (Bad market)
0	($1,500)	PV = Cashflow/(1+r)^n	($1,500)
1	$500	$500/(1+10%)^1 =$454.54	$25	$25/(1+10%)^1 =$22.72
2	$500	$500/(1+10%)^2 =$413.22	$25	$25/(1+10%)^2 =$20.66
3	$500	$500/(1+10%)^3 =$375.65	$25	$25/(1+10%)^3 =$18.78
4	$500	$500/(1+10%)^4 =$341.51	$25	$25/(1+10%)^4 =$17.07
5	$500	$500/(1+10%)^5 =$310.46	$25	$25/(1+10%)^5 =$15.52
6	$500	$500/(1+10%)^6 =$282.24	$25	$25/(1+10%)^6 =$14.11
7	$500	$500/(1+10%)^7 =$256.58	$25	$25/(1+10%)^7 =$12.82
	CUMULATIVE PRESENT VALUE CASHFLOW	$2434.19		$121.689
	NPV	$2,434.19-$1,500 =$934.19		$121.689-$1,500 ($1,378.31)

Expected NPV (without waiting for an year) = Probability of Good market conditions × NPV + Probability od bad Market condition × NPV of bad market

=75%×$934.19 + 25%×($1,378.31)

=$700.64+($344.58) =$356.06

Expected NPV (after waiting for an year) = NPV/(1+r)^1=$934.19/(1+10%)^1 =$849.26

The Expected NPV increased ($849.26 -$356.06 =$493.2) if NPC wait for an year

b) Coefficient of Variation = Volatility/ Expected Return

Volatility = Expected NPV (waiting for an year) - Expected NPV (proceeding Project today)

Volatility =$849.26 - $356.06 =$493.2

Expected Return= $849.26

Coefficient of Variation = $493.2/$849.26 ×100= 58.07%