Question

(a)Suppose you are the risk manager for a company considering a $5,250,000 investment in

a new 12-year project. The$5.25 million cost of the project will be depreciated on a straight-

line basis over 5 years. The project is expected to generate positive operating cash flows

equal to S1,600,000 per year(not including the effect of depreciation or taxes). The

company's tax rate is 21%. Ignoring any risk management considerations,evaluate the project

by calculating its net present value and internal rate of return. Assume the company has a

required return of 14%.

(b)As risk manager,you are concerned about the additional liability exposure the firm will

face if it accepts the project. You obtain an estimate of the annual total loss distribution froman insurance company that has many years of experience dealing with these types of

exposures. The annual total loss distribution has a mean of $190,000,a standard deviation of

$60,000,and a skewness coefficient of 2. The management team is worried about how the

potential liability losses will be financed. The company decides to establish a loss reserve

such that it can be 88%confident that its actual losses can be met by the fund. Determine the

size of the required loss reserve using the normal power approximation.

(c) Recalculate the net present value and internal rate of return for the project taking into

consideration the potential liability exposure and assuming a loss reserve is set up to handle

the losses. Any funds set aside in the reserve will earn interest at 2.5%per year.In addition,

the corporate risk manager estimates a "cost of worry” of $18,000.

Answer 1

1. Calculation of NPV :-

NPV = Inflow - Outflow

where outflow = $5.25 Mn

Inflow =

  

		1	2	3
Years	Cash Flows	Depriciation	Cash flow after dep	Tax @ 21%	Net Cash Flow (2+1-3)	Disc @14%	PV of cash flows
1	$ 1,600,000	$ 1,050,000	$                  550,000	$ 115,500	$                    1,484,500	0.88	$        1,302,193
2	$ 1,600,000	$ 1,050,000	$                  550,000	$ 115,500	$                    1,484,500	0.77	$        1,142,275
3	$ 1,600,000	$ 1,050,000	$                  550,000	$ 115,500	$                    1,484,500	0.67	$        1,001,995
4	$ 1,600,000	$ 1,050,000	$                  550,000	$ 115,500	$                    1,484,500	0.59	$            878,943
5	$ 1,600,000	$ 1,050,000	$                  550,000	$ 115,500	$                    1,484,500	0.52	$            771,003
6	$ 1,600,000		$              1,600,000	$ 336,000	$                    1,264,000	0.46	$            575,861
7	$ 1,600,000		$              1,600,000	$ 336,000	$                    1,264,000	0.40	$            505,142
8	$ 1,600,000		$              1,600,000	$ 336,000	$                    1,264,000	0.35	$            443,107
9	$ 1,600,000		$              1,600,000	$ 336,000	$                    1,264,000	0.31	$            388,690
10	$ 1,600,000		$              1,600,000	$ 336,000	$                    1,264,000	0.27	$            340,956
11	$ 1,600,000		$              1,600,000	$ 336,000	$                    1,264,000	0.24	$            299,084
12	$ 1,600,000		$              1,600,000	$ 336,000	$                    1,264,000	0.21	$            262,355

So, NVP = $7,911,604 - $5,250,000

= $2,661,604