Question

Today is 09/01/2020. Total earnings of S&P500 companies in the last 12 months amounted to 163. Total cash payout (Dividends + Buybacks) was 90% of the earnings. The expected earnings growth rate for each of the next 5 years (until 2025) is provided in the table below. After 2025 (t=5), earnings are assumed to grow at 1% per year forever. Assume the total cash payout ratio (Dividends + Buybacks as % of Earnings) will remain 90% forever. This implies that the total cash payout will increase at the same rate as the earnings.

	Last 12 Months	1	2	3	4	5
Expected Earnings Growth Rate		-25%	25%	17%	9%	3.5%
Expected Earnings	163	122.25	152.81	178.79	194.88	201.70
Expected Total Cash Payout (Dividends + Buybacks) as % of Earnings	90%	90%	90%	90%	90%	90%
Expected Total Cash Payout (Dividends + Buybacks)	146.70	110.03	137.53	160.91	175.39	181.35

a. If you invested $100 in the S&P500 on 1/1/1928, your investment would have grown to $502,176.01 by 12/31/2019 (92 years later). What is the compounded average annual return on the S&P500 from 1928 to 2019? (This is the return per year assuming compound interest.)

b. Suppose the required return (ie the cost of capital) on the S&P500 index is equal to your answer from part a. Calculate:

(i) the expected terminal value in 2025 (t = 5), that is the PV at t = 5 of the expected total cash payouts (dividends + buybacks) after t =5

(ii) the intrinsic value of the S&P500 index, that is the present value of all expected total cash payouts.

Answer 1

	Last 12 Months	1	2	3	4	5	6
Expected Earnings Growth Rate		-25%	25%	17%	9%	3.50%	1%	(Given)
Expected Earnings	$                163.00	$    122.25	$           152.81	$ 178.79	$ 194.88	$ 201.70	$     203.72
Expected Total Cash Payout in %	90%	90%	90%	90%	90%	90%	90%
Expected Total Cash Payout	$                146.70	$    110.03	$           137.53	$ 160.91	$ 175.39	$ 181.53	$     183.35
Intrinsic value						2106.218
Present Value		100.29163	114.27415	121.8729	121.0896	1439.71
Annual Compounded Interest	[(FV/PV)^(1/Time)]-1
Calculation	9.7051%	(a answer)
Answer B
(i)	Terminal Value of T5
Formula	D6/(cost of Capital- Growth)
Calculation	2106.217669
(ii)	Present Value of all expected cash Payouts
Formula	sum of cash flow n/ (1+cost of capital)^n
Calculation	1897.23857