Question

6.2     Complete the following table. Assume that the real interest rate is 3% per year, and inflation is expected to be constant at 2% per year. Recall that nominal cash flows must be discounted using nominal rates, and real cash flows must be discounted using real rates.                                                      

Year	Nominal cash flow	Real cash flow
0	–100,000	–100,000
1	+ 12,000
2	+22,000
3	+15,000
4	+10,000
Net present value
Discount rate		3%

Note that present values are taken at time 0, at which point real cash flows and nominal cash flows are the same, because there is no time for inflation to affect the cash flows.

This implies that the present values of the two series of cash flows should be exactly the same.

Hint: You may want to recall the $1 chocolate bar example from question 5.2 to assist you with calculating the real cash flows.

Note that you can use the CF function of the Texas Instruments BA II Plus calculator (similar on the HP 10BII series and Sharp EL738 series financial calculators) to calculate the NPV of these cash flows. See your user’s manual or a YouTube video to learn how to use this function.

Answer 1

In order to calculate Present Value of each cash flow, we can use following formula

N= no. of years

Discount rate for real cash flow=3%

Discount rate for nominal cash flow=(1+real rate) X (1+inflation) - 1

= (1.03) X (1.02) - 1 ==> 1.0506-1=0.0506 => 5.06%

Also, formula for Real cash flow

With all this information, now we can construct the table

	Nominal discount rate	5.06%	real discount rate	3.00%
Year	Nominal Cash flow	Nominal Cash flow present value	Real Cash flow	Real Cash flow present value
0	$       -100,000.0	$           -100,000.0	$ -100,000.0	$    -100,000.0
1	$           12,000.0	$               11,422.0	$     11,764.7	$        11,422.0
2	$           22,000.0	$               19,931.9	$     21,145.7	$        19,931.9
3	$           15,000.0	$               12,935.4	$     14,134.8	$        12,935.4
4	$           10,000.0	$                 8,208.2	$       9,238.5	$          8,208.2
Net Present Value= sum of all present value of cash flows		$           -47,502.47		$    -47,502.47

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