Question

QUE// Consider the historical data for an investment given in the accompanying table.

1. Calculate the total return (in dollars) for each year.
2. Indicate the level of return you would expect in 2018 and in 2019.
3. Comment on your forecast.

                                              Market value

Year           Income            Beginning              Ending

2013          $1.00               $30.00                   $32.50   

2014          $1.20               $ 32 .50                  $35.00

2015         $1.30                $35. 00                   $33.00

2016         $ 1.60               $ 33.00                   $40.00

2017         $ 1.75              $ 40.00                   $ 45.00

4. Refer to the table above, what is the total return in dollars and as a percentage of your original investment if you purchased 100 shares of investment at the beginning of 2013 and sold it at the end

of 2015?

Answer 1

Part (a)

Total return in a period = Market value at the end of the period - Market value at the beginning of the period + Income during the period = V_e - V_b + I

Please see the table below:

Year	Income ($)	Market Value at the beginning of the year ($)	Market Value at the end of the year ($)	Total Return ($)
	I	Vb	Ve	=Ve-Vb+I
2013	1.00	30.00	32.50	3.50
2014	1.20	32.50	35.00	3.70
2015	1.30	35.00	33.00	(0.70)
2016	1.60	33.00	40.00	8.60
2017	1.75	40.00	45.00	6.75
Total	6.85

Part (b)

There are multiple ways to forecast your return. We will resort to using compounded annual growth rate (CAGR) method.

g_I = CAGR in income from the year 2013 till the year 2017 = (I₂₀₁₇ / I₂₀₁₃)^(1/4) - 1 = 15.02%, say 15%

Please note that there are four years between 2013 and 2017.

So, expected income in 2018 = I₂₀₁₇ x (1 + g_I) = 1.75 x (1 + 15%) = $ 2.01, say $ 2.00

So, expected income in 2019 = I₂₀₁₈ x (1 + g_I) = 2.00 x (1 + 15%) = $ 2.30

g_v = CAGR in market value = (Value at the end of 2017 / Value at the beginning of 2013)^(1/5) - 1 = (45/30)^(1/5) - 1 = 8.45%

Please note that there are 5 years between start of 2013 till end of 2017.

So, expected market value at the end of 2018 = Value at the end of 2017 x (1 + g_v) = 45 x (1 + 8.45%) = $ 48.80, say $ 49

So, expected market value at the end of 2019 = Expected Value at the end of 2018 x (1 + g_v) = 48.80 x (1 + 8.45%) = $ 52.92, say $ 53

Hence expected level of return ($) in 2018 = I₂₀₁₈ + V₂₀₁₈ - V₂₀₁₇ = 2 + 49 - 45 = $ 6.00

Hence expected level of return ($) in 2019 = I₂₀₁₉ + V₂₀₁₉ - V₂₀₁₈ = 2.30 + 53 - 49 = $ 6.30

Part (c)

Every forecast has a finite probability, however small it may be, of going wrong. And my forecast is no exception. However the forecasts made here appear to be in line with what has happened historically. The inherent assumption in my forecast is there will no abnormal growth or degrowth in the macro environment. The things will continue to move the way they are. Usage of CAGR kind of normalises the fluctuation and noise in the prediction models. We could have used three years or two years moving average but there is no guarantee that those forecasts would have been anything better.

Part (d)

what is the total return in dollars and as a percentage of your original investment if you purchased 100 shares of investment at the beginning of 2013 and sold it at the end of 2015?

Total income from beginning of year 2013 till end of the year 2015 =  1.00 + 1.20 + 1.30 = $ 3.50

Increase in market value over this period = Value at the end of 2015 - value at the beginning of 2013 = 33 - 30 = $ 3

Hence, total return per share in dollars = 3.50 + 3 = $ 6.50

hence, total return for 100 shares = 100 x $ 6.50 = $ 650

Returns as %age of investment = Total return per share / Investment Price per share = 6.50 / 30 = 21.67%