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Unformatted text preview: 1 University of Essex Session 2011/12 Department of Economics Autumn Term EC111: INTRODUCTION TO ECONOMICS CAPITAL AND INVESTMENT Like labour, capital is a factor input. But because capital takes time to install it is a long run decision for the firm. The firm‘s decision is whether or not (and if so how much) to invest now in the expectation of returns (additional profits) in the future. This is a cost-benefit calculation. If the benefits exceed the (opportunity) costs then it is worth investing. But to make this calculation a way must be found to compare costs incurred now with benefits that accrue in the future. Present Values Suppose you invest £100 today in a project that will pay you: £55 one year from now, and £70 two years from now Should you invest? Note that £55 one year from today is worth less than £55 today. This is because you can put a smaller sum in the bank and accumulate interest, such that the total value in a year‘s time is £55. V 1 invested now would be worth V 1 (1+R) in a year‘s time, where R is the interest rate. If V 1 (1+R) = £55, then V 1 = £55/(1 +R). This is the Present Value of £55 in one year‘s time Similarly V 2 invested now would be worth V 2 (1+R)(1+R) in two years‘ time. So the present value £70 in two years‘ time is V 2 = £70/(1+R) 2 . The Net Present Value of the investment is the present value of the (future) benefits minus the (current) cost. Suppose the interest rate is 10 percent (0.1): 85 . 7 100 85 . 57 50 100 21 . 1 70 1 . 1 55 NPV The cost-benefit rule is that the investment is worth undertaking if the NPV is positive. 2 Note that: Future returns (or benefits) are discounted by the interest rate. The higher is the interest rate the more heavily they are discounted and the less likely the NPV will be positive. If the interest rate was 20 percent over these two years the NPV would not be positive. Q: what would it be? The further away are the future returns the more heavily they are discounted. Thus if the returns were nothing after one year £55 after two years and £70 after three years the NPV would be negative even at R = 0.1. Q: Check this calculation. The future benefits are expected returns , they are uncertain and therefore the discount factor used may need to take account of the riskiness of the project. What of there is inflation? £55 in a year‘s time has lower purchasing power if prices have risen than if they have not. In that case we need to discount by the real interest rate: Real interest rate = nominal interest rate – rate of inflation. The real interest rate is uncertain even if the nominal interest rate is not since we would need to forecast the rate of inflation over the lifetime of the investment....
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This note was uploaded on 03/15/2012 for the course EC 111 taught by Professor Timhatton during the Spring '12 term at Uni. Essex.
- Spring '12