Question

13. A bill that is designed to reduce the nation's budget deficit passes both houses of legislature. Congress tells us that the bill will reduce the deficit by $500 billion over 10 years. What it does not tell us is the timing of the reductions as shown below. Deficit Reduction $ 25 Billion $ 30 Billion $ 35 Billion $40 Billion $45 Billion $ 55 Billion $ 60 Billion $ 65 Billion $ 75 Billion $ 85 Billion Year 10 If the federal government can borrow at 8%, what is the true deficit reduction in the bill?

Answer 1

Here we will have to compute the present value of the deficit reduction by discounting the quantum of reduction for each year at a rate of 8% discount rate.

In other words the concept of net present value (NPV) will be used.

Year	Deficict reduction	1+r	PVIF	Present value of deficit reduction
1	25.00	1.08	0.9259	23.15
2	30.00		0.8573	25.72
3	35.00		0.7938	27.78
4	40.00		0.7350	29.40
5	45.00		0.6806	30.63
6	55.00		0.6302	34.66
7	60.00		0.5835	35.01
8	65.00		0.5403	35.12
9	75.00		0.5002	37.52
10	85.00		0.4632	39.37
			Total	318.36

Thus we can see that using the concept of time value of money the true deficit reduction in the bill is $318.36 billion.

Calculations:

PVIF = 1/1.08^n where n is the year of cash flow. For instance in year 2 PVIF = 1/1.08^2 = 0.8573

Present value of deficit reduction = actual amount*PVIF. For instance for year 2 present value = 30*0.8573 = 25.72

Total true deficit reduction = sum of all present values as computed above.