Question

Your best friend wants to borrow $2000 from you today for an emergency purchase they need to make that requires a cash payment. They promise to pay you back $1000 in 1 year (i.e. 12 months) and then pay you $1100 in two years (i.e. in 24 months). You would have to remove the money from your stock investment account which is earning on average a return of 5% (i.e. the effective yearly interest rate you are getting on your money is 0.05).
Required:
a. Is this a fair deal for you? Justify your answer with an engineering economics analysis and discussion of the situation by calculating the Net Present Value (NPV) for the scenario.
b. Draw a Cash Flow Diagram for this situation.

Answer 1

Answer:

a. It is not a fair deal for me.

The question is how much is $1,000 today when received in 12 months' time from now.  The present value of $1,000 at 5% effective interest rate is $952 ($1,000 * 0.952).  The other repayment of $1,100 in 2 years' time from now is worth $997.70 today at the 5% effective interest rate.  This implies that my friend is repaying me $1,949.70 in present value terms.

For friendship sake, I may lend her the money, but in economic analysis terms, the NPV value will yield a negative value of $50.30 ($2,000 - $1,949.70).  My friend is not actually paying me back the amount I would lend to her.  She is paying me less than I actually would lend to her.

b. Cash Flow Diagram:

                 Year 1             Year 2

                    F1                F2

                 $1,000          $1,100     (Inflows)

Fo⇵.................⇵.......................⇵...........................⇵n period

Year 0

$2,000   (outflows)

Explanation:

The cash flow diagram for this loan is the graphical representation of the timing of the cash flows with a clear marking of the repayments made by my best friend in two instalments and the $2,000 that I lent to her.  This cash flow diagram presents the flow of cash as arrows on a timeline scaled to the magnitude of the cash flow, where outflows are down arrows and inflows are up arrows.

The Net present value (NPV) of this loan shows the difference between the present value of repayments by my best friend and the present value of $2,000 that I lent to her over a period of 2 years. To obtain this difference, the present values of cash inflows  of $1,000 in a year's time and $1,100 in two years' time are determined using the discount factor table based on the given interest rate of 5%.