Repayment multiplier

The right-hand side of Equation (3.5) is known as the capital recovery factor or present worth factor, and the inverse of the right-hand side is known as the repayment multiplier r. 

Tables of the repayment multiplier are listed in handbooks and some textbooks. Table 3.1 gives r over some limited ranges as a function of n and i.

In Example 3.3 we developed an objective function for determining the optimal thickness of insulation. In that example the effect of the time value of money was introduced as an arbitrary constant value of r, the repayment multiplier. In this example, we treat the same problem, but in more detail. We want to determine the optimum insulation thickness for a 20-cm pipe carrying a hot fluid at 260°C. Assume that curvature of the pipe can be ignored and a constant ambient temperature of 27°C exists. The following information applies ... 

The capital charge factor (/3) multiplied by the capital cost of the plant (Co) gives the cost of servicing the total capital required. Suppose the capital costs of a plant at the beginning of the first year is Co and the plant has a life of N years so an annual amount must be provided which is (Co/ + B). The first term (CoO is the simple interest payment and the second (B) matures into the capital repayment after N years (i.e. interest added to the accumulated sum at the end of each year), thus... 

A bond s term to maturity is crucial because it indicates the period during which the bondholder can expect to receive coupon payments and the number of years before the principal is paid back. The principal of a bond—also referred to as its redemption value, maturity value, par value, or face value—is the amount that the issuer threes to repay the bondholder on the maturity, or redemption, date, when the debt ceases to exist and the issuer redeems the bond. The coupon rate, or nominal rate, is the interest rate that the issuer agrees to pay during the bond s term. The annual interest payment made to bondholders is the bond s coupon. The cash amount of the coupon is the coupon rate multiplied by the principal of the bond. For example, a bond with a coupon rate of 8 percent and a principal of 1,000 will pay an annual cash amount of 80. 

The economic comparison is based on the equivalent annual cost (EAC). The EAC is the cost per year of owning and operating an asset over its entire lifespan. EAC is often used as a decision-making tool in capital budgeting when comparing investment projects. The EAC can be calculated by multiplying the net present value (NPV) of a project by the loan repayment factor LRF. The loan repayment factor (LRF) is calculated by the total time n (years) of the project and the discount rate ( ). The net present value (NPV) of a project or investment is defined as the sum of the present values of the annual cash flows C, minus the initial investment Cq. 

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