Question

1. Rick is currently 35 years old. He plans to retire at age 65 and hopes to live to age 85. His labour income is $50,000 per year, and he intends to maintain a constant level of real consumption spending over the next 50 years. Assuming a real interest rate of 3% per year, no taxes, and no growth in real labour income, what is the value of Rick’s human capital?

****I would like this broken down step by step, and the formula that was used for it****

Answer 1

Rick earns $50000 per year and he will continue to earn so for the next 30 years, therefore his human capital should be such an amount that grows @ 3% and gets reduced annually by $50000 would last for 30 years which will basically be the PV of 30 years of annual income of $50000 discounted at 3%.

We approach this problem step-wise

Step 1 If Rick's annual income is $50000 and real interest rate is 3%, it means that Rick is worth an asset that would yield $50000 per year @ 3% yield for 30 years.

Step 2 Value of Rick's Human capital = 50000 x PVAF (3%,30)

= 50000 x 19.60

= $980000

Step 3 Proof of the above calculation is shown in the following table where the abovementioned value i.e $1286488 is grown @3% and reduced by $50000 annually is shown lasting for 30 years.

	Opening	Interest @ 3%	Reduction	Closing
Year 1	980000.00	29400.00	50000.00	959400.00
Year 2	959400.00	28782.00	50000.00	938182.00
Year 3	938182.00	28145.46	50000.00	916327.46
Year 4	916327.46	27489.82	50000.00	893817.28
Year 5	893817.28	26814.52	50000.00	870631.80
Year 6	870631.80	26118.95	50000.00	846750.76
Year 7	846750.76	25402.52	50000.00	822153.28
Year 8	822153.28	24664.60	50000.00	796817.88
Year 9	796817.88	23904.54	50000.00	770722.41
Year 10	770722.41	23121.67	50000.00	743844.09
Year 11	743844.09	22315.32	50000.00	716159.41
Year 12	716159.41	21484.78	50000.00	687644.19
Year 13	687644.19	20629.33	50000.00	658273.52
Year 14	658273.52	19748.21	50000.00	628021.72
Year 15	628021.72	18840.65	50000.00	596862.37
Year 16	596862.37	17905.87	50000.00	564768.25
Year 17	564768.25	16943.05	50000.00	531711.29
Year 18	531711.29	15951.34	50000.00	497662.63
Year 19	497662.63	14929.88	50000.00	462592.51
Year 20	462592.51	13877.78	50000.00	426470.29
Year 21	426470.29	12794.11	50000.00	389264.39
Year 22	389264.39	11677.93	50000.00	350942.33
Year 23	350942.33	10528.27	50000.00	311470.60
Year 24	311470.60	9344.12	50000.00	270814.71
Year 25	270814.71	8124.44	50000.00	228939.15
Year 26	228939.15	6868.17	50000.00	185807.33
Year 27	185807.33	5574.22	50000.00	141381.55
Year 28	141381.55	4241.45	50000.00	95623.00
Year 29	95623.00	2868.69	50000.00	48491.69
Year 30	48491.69	1508.31	50000.00	0.00