### Discounted Cash Flow Factors

• Calculate present and future values of various payment methods such as single payment, uniform series, gradient series using formulae and vales extracted from table.

• Estimate and compare rate of returns on different investment proposals.

### Solved Example:

An investor deposits \$1,000 in June in an initially empty account paying monthly 7%, and then makes withdrawals of \$400 and \$500 in July and August. What will be the compound amount of these cash flows in October using the compound amount formula? Solution: Time value of \$1000 after 4 months = $1000 \times \left(1 + \dfrac{7}{100}\right)^4 = \$1310.80$Time value of \$400 after 3 months $= 400 \times \left(1 + \dfrac{7}{100}\right)^3 = \$490.02$Time value of \$500 after 2 months $= 500 \times \left(1 + \dfrac{7}{100}\right)^2 = \$572.45$Net value after all transactions $= \1310.80 - \490.02 - \572.45 = \248.35$ Correct Answer: A ### Solved Example: #### 15-1-02 A company received a buy-out offer where it is offered \$37,000 now or \$45,000 after 3 years. If the interest rate is 6% per annum, which offer should it accept? Solution: We will calculate the present value of \$45,000. $F = P \left( 1 + \dfrac{r}{100} \right) ^t$ \begin{align*} P &= \dfrac{F}{\left( 1 + \dfrac{r}{100} \right) ^t}\\ &= \dfrac{45000}{\left( 1 + \dfrac{6}{100} \right) ^3}\\ &= \dfrac{45000}{(1.06)^3}\\ &= 37,782.87 \end{align*} So, the present value of \$45,000 now is \$37,782.87 which is higher than \$37,000. Hence, the company should accept \$45,000 after 3 years.
Note: Alternatively, you may calculate the future value of \$37,000 after 3 years and compare it with \$45,000.