Air Products & Chemicals Inc. (NYSE:APD)

Dividend Discount Model (DDM)

Intermediate level

In discounted cash flow (DCF) valuation techniques the value of the stock is estimated based upon present value of some measure of cash flow. Dividends are the cleanest and most straightforward measure of cash flow because these are clearly cash flows that go directly to the investor.

Intrinsic Stock Value (Valuation Summary)

Air Products & Chemicals Inc., dividends per share (DPS) forecast

US\$

Year Value DPSt or Terminal value (TVt) Calculation Present value at 10.87%
0 DPS01 5.18
1 DPS1 5.55 = 5.18 × (1 + 7.17%) 5.01
2 DPS2 5.97 = 5.55 × (1 + 7.61%) 4.86
3 DPS3 6.45 = 5.97 × (1 + 8.04%) 4.74
4 DPS4 7.00 = 6.45 × (1 + 8.47%) 4.63
5 DPS5 7.62 = 7.00 × (1 + 8.90%) 4.55
5 Terminal value (TV5) 422.25 = 7.62 × (1 + 8.90%) ÷ (10.87%8.90%) 252.10
Intrinsic value of Air Products & Chemicals Inc.’s common stock (per share) \$275.89
Current share price \$286.91

Based on: 10-K (filing date: 2020-11-19).

1 DPS0 = Sum of the last year dividends per share of Air Products & Chemicals Inc.’s common stock. See details »

Disclaimer!
Valuation is based on standard assumptions. There may exist specific factors relevant to stock value and omitted here. In such a case, the real stock value may differ significantly form the estimated. If you want to use the estimated intrinsic stock value in investment decision making process, do so at your own risk.

Required Rate of Return (r)

 Assumptions Rate of return on LT Treasury Composite1 RF 1.66% Expected rate of return on market portfolio2 E(RM) 12.16% Systematic risk of Air Products & Chemicals Inc.’s common stock βAPD 0.88 Required rate of return on Air Products & Chemicals Inc.’s common stock3 rAPD 10.87%

1 Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).

3 rAPD = RF + βAPD [E(RM) – RF]
= 1.66% + 0.88 [12.16%1.66%]
= 10.87%

Dividend Growth Rate (g)

Dividend growth rate (g) implied by PRAT model

Air Products & Chemicals Inc., PRAT model

Average Sep 30, 2020 Sep 30, 2019 Sep 30, 2018 Sep 30, 2017 Sep 30, 2016 Sep 30, 2015
Selected Financial Data (US\$ in thousands)
Dividends on common stock 1,144,100  1,008,300  931,800  808,500  733,700  687,900
Net income attributable to Air Products 1,886,700  1,760,000  1,497,800  3,000,400  631,100  1,277,900
Sales 8,856,300  8,918,900  8,930,200  8,187,600  9,524,400  9,894,900
Total assets 25,168,500  18,942,800  19,178,300  18,467,200  18,055,300  17,438,100
Total Air Products shareholders’ equity 12,079,800  11,053,600  10,857,500  10,086,200  7,079,600  7,249,000
Financial Ratios
Retention rate1 0.39 0.43 0.38 0.73 -0.16 0.46
Profit margin2 21.30% 19.73% 16.77% 36.65% 6.63% 12.91%
Asset turnover3 0.35 0.47 0.47 0.44 0.53 0.57
Financial leverage4 2.08 1.71 1.77 1.83 2.55 2.41
Averages
Retention rate 0.48
Profit margin 15.47%
Asset turnover 0.47
Financial leverage 2.06

Dividend growth rate (g)5 7.17%

Based on: 10-K (filing date: 2020-11-19), 10-K (filing date: 2019-11-26), 10-K (filing date: 2018-11-20), 10-K (filing date: 2017-11-16), 10-K (filing date: 2016-11-21), 10-K (filing date: 2015-11-24).

2020 Calculations

1 Retention rate = (Net income attributable to Air Products – Dividends on common stock) ÷ Net income attributable to Air Products
= (1,886,7001,144,100) ÷ 1,886,700
= 0.39

2 Profit margin = 100 × Net income attributable to Air Products ÷ Sales
= 100 × 1,886,700 ÷ 8,856,300
= 21.30%

3 Asset turnover = Sales ÷ Total assets
= 8,856,300 ÷ 25,168,500
= 0.35

4 Financial leverage = Total assets ÷ Total Air Products shareholders’ equity
= 25,168,500 ÷ 12,079,800
= 2.08

5 g = Retention rate × Profit margin × Asset turnover × Financial leverage
= 0.48 × 15.47% × 0.47 × 2.06
= 7.17%

Dividend growth rate (g) implied by Gordon growth model

g = 100 × (P0 × rD0) ÷ (P0 + D0)
= 100 × (\$286.91 × 10.87%\$5.18) ÷ (\$286.91 + \$5.18)
= 8.90%

where:
P0 = current price of share of Air Products & Chemicals Inc.’s common stock
D0 = the last year dividends per share of Air Products & Chemicals Inc.’s common stock
r = required rate of return on Air Products & Chemicals Inc.’s common stock

Dividend growth rate (g) forecast

Air Products & Chemicals Inc., H-model

Year Value gt
1 g1 7.17%
2 g2 7.61%
3 g3 8.04%
4 g4 8.47%
5 and thereafter g5 8.90%

where:
g1 is implied by PRAT model
g5 is implied by Gordon growth model
g2, g3 and g4 are calculated using linear interpoltion between g1 and g5

Calculations

g2 = g1 + (g5g1) × (2 – 1) ÷ (5 – 1)
= 7.17% + (8.90%7.17%) × (2 – 1) ÷ (5 – 1)
= 7.61%

g3 = g1 + (g5g1) × (3 – 1) ÷ (5 – 1)
= 7.17% + (8.90%7.17%) × (3 – 1) ÷ (5 – 1)
= 8.04%

g4 = g1 + (g5g1) × (4 – 1) ÷ (5 – 1)
= 7.17% + (8.90%7.17%) × (4 – 1) ÷ (5 – 1)
= 8.47%