Question

In planning for your retirement, you are considering the various CPF LIFE annuity plans. For the Basic Retirement Plan (BRP), the sum required upfront is $85,500 and it pays out $750 monthly for as long as you live. Alternatively, the Enhanced Retirement Plan (ERP) requires a sum of $256,500 and the monthly payout is $2,000. For both annuity plans, interest earned is 4% per annum and payout is made at the end of each month when you turn 65.
To help you save up for the sum required in the annuity plan, you are considering investing in a 6% coupon (paid semi-annually) corporate bond that matures in 8 years at par of $1,000. It currently trades at $945 and you expect a return of 7% per year.
(a) Calculate the minimum number of years you need to receive the payout for the basic retirement plan for it to be worth it.

(b) Determine which annuity plan is better assuming you are able to live up to 85.
(c) Appraise whether you should invest in the corporate bond today.
(d) Describe three (3) factors that will affect the expected return on the corporate bond.

Answer 1

Part a

Annuity formula is given by

PV = E(1-(1+r)^-p)/r

Where

PV = present worth= 85500

E = monthly payout= 750

r= monthly rate= 4%/12= .3333%

p= total duration in months = ??

Therefore

85500= 750(1-1.00333^-p)/.00333333

P= 143.65 months or 143.64/12 =11.97 years or 12 years

Part b

These plan will start paying off after 65 and they will keep running for 20 years let us calculate thier worth one by one

P= 12 ×20= 240

Basic plan:

Worth = 750(1-1.003333^-240)/.0033333 = 123766

Which is higher then upfront cost by 123766-85500= 38266

Enhanced plan :

Worth= 2000(1-1.003333^-240)/.00333333 = $330044 which is greater then upfront cost by 330044- 256500 = 73543

Enhanced plan is better since benifit in this plan is higher.

Part c

Let us calculate the price of this bond

P0= I(1-(1+r)^-p)/r + F/(1+r)^p

Where

I = semi annual coupon payment = 1000×.06× 1/2 =30$

r= semiannual yield = 7%/2 = 3.5%

P= semiannual period = 2 ×8 = 16

F face value =1000

Therefore

P0= 30(1-1.035^-16)/.035 + 1000/1.035^16 = 939

Investment in bond is not viable as the bond is overpriced ( actual price is higher then theoretical price).

Part d

There are many factors that may affect a bond some of them are

Inflation: if expected inflation is higher then real return form the bond will decrease.

Issuer's credit worthiness: if issuer is risky then then bondholders would require higher returns.

Liquidity: longer rhe duration of bond, Higher required and expected returns.

Economic stability: if there is a stability in the economy then people will start moving towards the equity market for higher returns.

Monetary policy: if there is an expansionary monetary policy then people will start investing thier money in bond.