Question

Question A3 Christy just won the Mark Six. She must choose one of the following three award options.

Option 1: receive a lump sum today of $65 million

Option 2: receive 10 end-of-year payments of $9.5 million

Option 3: receive 30 begin-of-year payments of $5.5 million

Required: a. If she thinks she could earn 7% annually, advise her which option she should choose.

b. If she expects the interest rate will increase, advise her which option she should choose. (Total 6 marks)

Answer 1

Answer :a.)   If she thinks she could earn 7% annually , Option to be choosen

Option 1 : Receive a lump sum today of $65 million

Lump sum today of $65 million

Present Value = $65 million

Option 2:Receive 10 end-of-year payments of $9.5 million

$9.5 miilion end of the year payments for 10 years

Present Value = 9.5 million * PVAF @ 7% for 10 years

= 9.5 million * 7.0236

= 66.7242 million

Option 3:Receive 30 begin-of-year payments of $5.5 million

Present Value = 5.5 million * [( PVAF @ 7% for 29 years ) + 1 ]

= 5.5 million * (12.2777 + 1)

= 5.5 million * 13.2777

= 73.02735 million

So, Christy should choose Option 3 as its present value is maximum.

(b.)Advise on the option when interest rate increases

Now let us suppose interest rate increases to 8%

Option 1: Receive a lump sum today of $65 million

Lump sum today of $65million

Present Value = $65 million

Option 2:Receive 10 end-of-year payments of $9.5 million

$9.5 miilion end of the year payments for 10 years

Present Value = 9.5 million * PVAF @ 8% for 10 years

= 9.5 million * 6.7101

= 63.74595 million

Option 3:Receive 30 begin-of-year payments of $5.5 million

Present Value = 5.5 million * [( PVAF @ 8% for 29 years ) + 1 ]

= 5.5 million * (11.1584 + 1)

= 5.5 million * 12.1584

= 66.8712 million

So, Christy should choose Option 3 as its present value is maximum when interest rate becomes 8 %

Now let us suppose interest rate increases to 8.34%

Option 1: Receive a lump sum today of $65 million

Lump sum today of $65million

Present Value = $65 million

Option 2:Receive 10 end-of-year payments of $9.5 million

$9.5 miilion end of the year payments for 10 years

Present Value = 9.5 million * PVAF @ 8.34% for 10 years

= 9.5 million * 6.6084

= 62.7798 million

Option 3: Receive 30 begin-of-year payments of $5.5 million

Present Value = 5.5 million * [( PVAF @ 8.34% for 29 years ) + 1 ]

= 5.5 million * (10.8156 + 1)

= 5.5 million * 11.8156

= 64.9858 million or 65 million

Note : Difference is due to rounding off of Present value factor as only for illustration purpose

So, Christywould become indifferent whether to choose Option 1 or Option 3 as its present value is maximum when interest rate becomes 8.34 %

Now let us suppose interest rate increases to 9%

Option 1: Receive a lump sum today of $65 million

Lump sum today of $65million

Present Value = $65 million

Option 2:Receive 10 end-of-year payments of $9.5 million

$9.5 miilion end of the year payments for 10 years

Present Value = 9.5 million * PVAF @ 9% for 10 years

= 9.5 million * 6.4177

= 60.96815 million

Option 3:Receive 30 begin-of-year payments of $5.5 million

Present Value = 5.5 million * [( PVAF @ 9% for 29 years ) + 1 ]

= 5.5 million * (10.1983+ 1)

= 5.5 million * 11.1983

= 61.59065 million

So, Christy should choose Option 1 as its present value is maximum when interest rate becomes 8 %

So we can see three different scenarios which is that if interest rate increases upto 8.34% Christy would Choose option 3.

If interest rate is somewhere around 8.34% then Christy would choose either option 3 or option 1

But if interest rate increase Beyond 8.34% then Christy should choose Option 1