Question

On present-discounted values and investment decisions Jesse and Wally are new business partners who confider building a Brownie factory. The following table 1 2 gives the net profits that they expect to receive at the each of each year with certainty. The yield to maturity of a four-year bond is presently i4t = 3%. Assume that this 3% also corresponds to the one-year expected interest rates over the four years. There is no inflation and the factory becomes obsolete after its fourth year of operation. ? e t ? e t+1 ? e 1,t+2 ? e 1t+3

Expected net profit 100 150 200 200

(a) What is the maximum price that Jesse and Wally are willing to pay in order to build the factory

(b) Suppose that the expected, short-term one year interest rate for the fourth year increases from an initial value of i1t+3 = 3% to a new value of i1t+3 = 5%. All else remains equal. Recalculate the maximum building cost required in order to implement the project. What does this say about the effect of an increase in expected short-term interest rates on the investment levels today?

(c) Suppose that a suddenly gloomier outlook leads Jesse and Wally to revise down their expected profits in the third and fourth year to decrease to ? e 1t+2 = ? e 1t+3 = 150. All else remains equal. Recalculate the maximum building cost required in order to implement the project. What does this say about the effect of a gloomier outlook about the future on the investment levels today?

Answer 1

Here it is silent about the tax applicable to Jesse and Wally in the Question. So it is assumed that they are taxed @zero. Since tax is not applicable the Depreciation also doesnot have role in this situation. The Dpreciation is relevant only if the Organization has to pay tax, otherwise there will not be any tax savings on depreciation. the given net profits are assumed to be the net profit before dapreciation.

Answer to Question a,

In Capital budgetting decision making, if cash flows are certain, the cashflows are discounted by using risk free rate or interest to arrive present value,

So the Maximum price to pay is the present value of net profit before depreciation. It will reflect the cash flow in this scenario without Tax.

Present Value = Annual cash flow x discount factor,

Discount factor = 1/(1+i)ⁿ, here " i " is the interest rate = 3%, "n" is the corresponding year.

Years	Cash flow	Discount Factor		Present Value
1	100	0.970873786407767		97.087378640776700
2	150	0.942595909133754		141.389386370063000
3	200	0.915141659353159		183.028331870632000
4	200	0.888487047915689		177.697409583138000
	Total Present Value			599.202506464610000

The maximum price that Jesse and Wally are willing to pay is $599.202506464610000, Rounded to 2 decimal places = $599.20.

Answer to Question b,

Present Value = Annual cash flow x discount factor,

Discount factor = 1/(1+i)ⁿ, here " i " is the interest rate = 3%, but in the 4^th year i = 5%, and formula in the 4^th year will be 1/((1.03)³ X(1.05)). "n" is the corresponding year.

Years	Cash flow	Discount Factor		Present Value
1	100	0.970873786407767		97.087378640776700
2	150	0.942595909133754		141.389386370063000
3	200	0.915141659353159		183.028331870632000
4	200	0.871563485098247		174.312697019649000
	Total Present Value			595.817793901121000

The maximum price that Jesse and Wally are willing to pay is $595.817793901121000, Rounded to 2 decimal places = $595.82.

The effect of an increase in expected short-term interest rates is resulted to reduce the Investment amount. Before the change the maximum amount willing to pay was $599.20 before knowing the increase in interest rate , but the maximum amount willing to pay is reduced to $595.82 after knowing the increase in interest rate.

Answer to Question c,

The revised profits in year3 & year 4 (e 1t+2 = 150 , e 1t+3 = 150) is $150. then the Maximum amount willing to pay is $509.021071101167000, rounded to 2decimal places =$509.02.

Years	Cash flow	Discount Factor		Present Value
1	100	0.970873786407767		97.087378640776700
2	150	0.942595909133754		141.389386370063000
3	150	0.915141659353159		137.271248902974000
4	150	0.888487047915689		133.273057187353000
	Total Present Value			509.021071101167000

The effect of a gloomier outlook about the future on the investment also resulted to reduce the Value of Investment today. Before the change the maximum amount willing to pay was $599.20 before estimating the gloomier outlook, but the maximum amount willing to pay is reduced to $509.02 after estimating gloomier outlook.

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