Question

3 Problem Set: The NPV Rule 1 In Figure 1, the sloping straight line represents the opportunities for investment in the capital market, and the solid curved line represents the opportunities for investment in plant and machinery (real nassets). The company's only asset at present in $2.6 million in cash $ tomorrovw Owners prefenned consumption pastern 3.75 1 16 26 4 today Figure 1: This graph is used in problem #1 (a) What is the interest rate? (b) How much should the company invest in plant and machinery? (c) How much will this investment be worth next year? (d) What is the average rate of return on the investment? (e) What is the marginal rate of return? (f) What is the present value of this investment? (g) What is the net present value of this investment? (h) What is the total present value of the company? (i) How much will the individual consume today? G) How much will he consume tomorrow? (k) Is he a borrower or a lender? 2. A firm starts out with $10 million in cash. The rate of interest between now and later (the only two periods) s 15%. To invest in all the available positive NPV projects, the firm had to invest $4 million in real assets. The total prsent value (not NPV) of these projects is $7 million. Answer the following questions:

Answer 1

You have asked a question with multiple sub parts. I have addressed the first four of them. Please do post the balance sub parts as separate question.

All financials are in $ mn.

Q - 1

(a) For interest rate look at the capital markets line. $ 4 today becomes $ 5 tomorrow. Let i be the interest rate.

Hence, 4 x (1 + i) = 5; hence, i = 5 / 4 - 1 = 25%

(b) Locate the point of tangency. At the point of tangency, investment in capital market = 1.6

Hence investment in plant & machinery = 2.6 - 1.6 = $ 1.0 mn

(c) Read the value of $ tomorrow corresponding to the point of tangency. It's 3.0.

This $ 1.0 mn gives $ 3.0 mn next year.

(d) Hence, return = 3 / 1 - 1 = 200%