Question

2. Alberto Inc. just paid its annual dividend of $2.00 per share. The firm is expected to grow at a rate of 10 percent for the next two years and then at 6 percent per year thereafter. The required return of Alberto Inc. is 12%. Find the expected price of the stock in one year, P1.
3. The table below is the YTM of U.S. Treasuries with different maturities on April 1, 2020.

1 yr.	2 yr.	3 yr.	5 yr.	7 yr.
0.16%	0.23%	0.28%	0.37%	0.51%

1. What is the expected two-year rate in three years according to the Pure Expectations Theory?                                                    
2. What is an inverted yield curve? Give one reason that may cause the yield curve to invert.                                                                 

Answer 1

Solution 1) Recent paid dividend (D0) = $2

Dividend growth for two years = 10%

Dividend growth after two years = 6%

The required rate of return (r) = 12%

For the high growth period, the dividends are calculated as follows:

Dividend in 1 year (D1) = D0*(1+10%) = 2*(1+10%) = $2.2

Dividend in year 2 (D2) = D1*(1+10%) = 2.2*(1+10%) = $2.42

Dividend in year 3 (D3) = D2*(1+6%) = 2.42*(1+6%) = $2.57

Year 3 onwards, the dividends grow at a constant rate of 6%

Present Value of perpetuity = Next year dividend/(r - g)

The present value of cash flows (at t=2) = D3/(r - g)

= 2.57/(12% - 6%) = $42.75

The calculation is shown below:

The stock price at t=1 is calculated as:

Expected stock price in one year (P1) = $42.53

Solution 2) a) 3-year spot rate (S2) = 0.28%

n2 = 3

5-year spot rate (S1) = 0.37%

n1 = 5

The forward rate is calculated as following

Forward Rate = [(1 + S1)n1 / (1 + S2)n2]1/(n1-n2) – 1

Forward rate = [(1+0.37%)^5/(1+0.28%)^3]^[(1/(5-3)] - 1

= [(1.0037)^5/(1.0028)^3]^(1/2) - 1

= [(1.01864)/(1.0084)]^(1/2)-1

= (1.01013)^(0.5) - 1

= 1.00505 - 1

= 0.51%

Solution 2) b) An inverted yield curve occurs when the short term interest rates are more than the long term interest rates. This implies that an investor will have high returns by investing in the short term while there will be low returns in the long term.

One of the possible reasons for the inverted yield curve is when the investors are having low confidence in the growth of the economy and it is believed that the economy is entering into a recession.