Question

Your firm recently divested some non-core assets and now has a significant amount of excess cash. Branda Sim, the CEO, is considering investing in either Singapore Technologies Engineering Limited (“STE”) shares or 10-year Singapore Government Securities (“SGS”) or a combination of both. She knows that you are studying a Finance course, and she is seeking your advice.

Based on your research, the following market data was obtained:

Information relating to STE

Date	Share Price ($)	Dividends Per Share (Cents)
31-Dec-13	3.59	15
31-Dec14	3.25	15
31-Dec-15	2.83	15
31-Dec-16	3.30
31-Dec-17	3.37	0.15
31-Dec-18	3.72	0.15

As at December 2018, beta is 0.72.

Information relating to SGS

Date	Bond Price
31-Dec-13	101.61
31-Dec14	106.21
31-Dec-15	98.15
31-Dec-16	97.08
31-Dec-17	112.47
31-Dec-18	104.94

The coupon rate is 2.75% per year and will mature in December 2023.

Other market data

• Market risk premium = 5.5%

• Inflation rate = 1.2%

(a) Calculate the annual returns for both STE and SGS for the 5 years 2014 to 2018.   

Answer 1

Annual returns for STE

Annual returns for a stock is made of 2 components: Price appreciation i.e. capital gains or losses and dividends.

Nominal Annual Returns = (Price at end of year - Price at beginning of year ) + Dividends

Real annual return = Nominal annual return - Inflation rate

For 2014 : Nominal Annual Returns = (3.25 - 3.59) + $ 0.15 = $ - 0.19

Nominal Annual returns % = - 0.19 / 3.59 = - 0.0529 = - 5.29%

Real Annual returns = - 5.29% - 1.2 % = - 6.49 %

For 2015: Nominal Annual Returns = (2.83 - 3.25) + $ 0.15 = - $ 0.27

Nominal Annual returns % = - 0.27 / 3.25 = - 0.0831 = - 8.31 %

Real Annual Returns = - 8.31 - 1.2 = - 9.51 %

For 2016: Nominal Annual Returns = (3.30 - 2.83) + 0 = $ 0.47  

Nominal Annual returns % = 0.47 / 2.83 = 0.1661 = 16.61%

Real Annual Returns = 16.61 - 1.2 = 15.41 %

For 2017: Nominal Annual Returns = (3.37 - 3.30) + $ 0.15 = $ 0.22  

Nominal Annual returns % = 0.22 / 3.30 = 0.0667 = 6.67 %

Real Annual returns % = 6.67 - 1.2 = 5.47 %

For 2018: Nominal Annual Returns = (3.72 - 3.37) + $ 0.15 = $ 0.5

Nominal Annual returns % = 0.5 / 3.37 = 0.1484 = 14.84 %

Real annual returns = 14.84 - 1.2 = 13.64 %

Nominal Annual return on STE from 2014 to 2018 = ( - 5.29 - 8.31 +16.61 + 6.67 +14.84) / 5 = 4.904 %

Real annual return on STE from 2014 to 2018 = ( - 6.49 - 8.31 + 15.41+ 5.47 +13.64 ) /5 = 3.944 %

Annual return on SGS

Coupon payment = $ 2.75 , Face value = $ 100

Annual return for a bond is calculated by finding the yield-to-maturity (YTM).

Formula for YTM is :

Current Bond Price= Coupon/(1+YTM) + Coupon/(1+YTM)² + Coupon/(1+YTM)³ + ...+ Coupon/(1+YTM)^N +

+ Face Value / (1+YTM)^N

For 2014: 101.621 = 2.75 / (1+y) + 2.75 / (1+y)² +...+ 2.75/(1+y)¹⁰ + 100 / (1+y)¹⁰

From above : y = 30.77 %

Nominal annual return for 2014 = 30.77 %

Real annual return for 2014 = 30.77 - 1.2 = 29.57 %

For 2015: 106.21 = 2.75 / (1+y) + 2.75 / (1+y)² +...+ 2.75/(1+y)⁹ + 100 / (1+y)⁹

From above : y = 23.87 %

Nominal annual return for 2015 = 23.87 %

Real annual return for 2015 = 23.87 - 1.2 = 22.67 %

For 2016: 98.15 = 2.75 / (1+y) + 2.75 / (1+y)² +...+ 2.75/(1+y)⁸ + 100 / (1+y)⁸

From above : y = 30.77 %

Nominal annual return for 2016 = 36.16 %

Real annual return for 2016 = 36.16 - 1.2 = 34.96 %

For 2017: 112.47 = 2.75 / (1+y) + 2.75 / (1+y)² +...+ 2.75/(1+y)⁷ + 100 / (1+y)⁷

From above : y = 10.84 %

Nominal annual return for 2017 = 10.84 %

Real annual return for 2017 = 10.84 - 1.2 = 9.64 %

For 2018: 104.94 = 2.75 / (1+y) + 2.75 / (1+y)² +...+ 2.75/(1+y)⁶ + 100 / (1+y)⁶

From above : y = 22.46 %

Nominal annual return for 2018 = 22.46 %

Real annual return for 2018 = 22.46 - 1.2 = 21.26 %