**Time Value of Money**

**Problem Set 6**

5. Given Smolira Golf Corp.βs recent Financial Statements in the next page:

A. Find the following financial ratios

(use year-end figures rather than average values where appropriate):

4. A financial planning service offers a college savings program. The plan calls for you to make six annual payments of Php 50,000 each, with the first payment occurring today,

your childβs 12th birthday. Beginning on your childβs 18th birthday, the plan will provide Php 150,000 per year for four years.

What return is this investment offering?

PVA=Php 150,000( 1β1(1+π)4π) FVA=Php 50,000((1+π)6β1π)

Thus, if PVA = FVA then:

Php 150,000( 1β1(1+π)4π)=

Php 50,000((1+π)6β1π)

r = 0.1452116585 or 14.52%

1. A 5-year annuity of ten Php 40,000 semi-annual payments will begin 9 years from now,

with the first payment coming 9.5 years from now.

If the discount rate is 14 percent compounded monthly:

semi-annual interest rate = (1+annual rate)^1/2 - 1

= (1+0.01167)^1/2 - 1

= 0.07209 or 7.2%

PV = 40,000 {[1-(1/1.072)^10]}/0.072

= 278364.23

2. Youβve just won the PCSO Lottery. Lottery officials offer you the choice of two alternative payouts: either Php 20 million today, or Php 30 million 10 years from now.

Which payout will you choose:

A. If the relevant discount rate is 0 percent?

3. You just bought a new car for

Php 900,000 on installment with no down payment, at 13% interest per year, payable in 60 equal monthly installments.

The first payment is due 1 month from now.

How much will be your total monthly payment amount?

Ordinary Annuity:

π=πΉπ(π)[(1+π)π]β1

π=900,000(.13/12)[(1+.13/12)60]β1

π=9,749.99970.908856497

π·=π·ππ πππππ.ππ

**Angeles**

Austria

Cortel

Dimaano

Fernandez

Ramos

Reyes

Rosales

Austria

Cortel

Dimaano

Fernandez

Ramos

Reyes

Rosales

A. What is the value of this annuity

five years from now?

C. What is the current value of the annuity?

B. What is the value three years

from now?

PV= 278,364.23/ (1.072)^8

= 159608.18

PV= 278,364.23/ (1.072)^12

= 120858.17

PV= 278,364.23 / (1.072)^18

= 79,635.61

B. If it is 10 percent?

C. If it is 20 percent?

CONGRATULATIONS!

Today

In 10 years

A. r = 0%

20 million today vs. 30 million today

PV = FV / (1+r)n

= 30 000 000 / 110

= 30 000 000

Php 20 000 000 < Php 30 000 000

20 million in 10 yrs vs. 30 million in 10 yrs

FV = PV * (1+r)n

= 20 000 000 * (1+0)10

= 20 000 000

Php 20 000 000 < Php 30 000 000

ANSWER

: 30 MILLION IN 10 YEARS

B. r =10%

Using the Computational Formula:

20 million today vs. 30 million today

PV = FV / (1+r)n

= 30 000 000 / (1+0.10)10

= 11 566 298.68

Php 20 000 000 > Php 11 566 298.68

20 million in 10 yrs vs. 30 million in 10 yrs

FV = PV * (1+r)n

= 20 000 000 * (1+0.10)10

= 51 874 849.2

Php 51 874 849.2 > Php 30 000 000

Using the Present Value and Future Value Interest Factors:

20 million today vs. 30 million today

PVIF10%,10 = 0.3855 * 30 000 000

= 11 565 000

Php 20 000 000 > Php 11 565 000

20 million in 10 yrs vs. 30 million in 10 yrs

FVIF10%,10 = 2.5937 * 20 000 000

= 51 874 000

Php 51 874 000 > Php 30 000 000

ANSWER

: 20 MILLION TODAY

C. r=20%

Using the Computational Formula:

20 million today vs. 30 million today

PV = FV / (1+r)n

= 30 000 000 / (1+0.20)10

= 4 845 167.487

Php 20 000 000 > Php 4 845 167.487

20 million in 10 yrs vs. 30 million in 10 yrs

FV = PV * (1+r)n

= 20 000 000 * (1+0.20)10

= 123 834 728.4

Php 123 834 728.4 > Php 30 000 000

Using the Present Value and Future Value Interest Factors:

20 million today vs. 30 million today

PVIF20%,10 = 0.1615 * 30 000 000

= 4 845 000

Php 20 000 000 > Php 4 845 000

20 million in 10 yrs vs. 30 million in 10 yrs

FVIF20%,10 = 6.1917 * 20 000 000

= 123 834 000

Php 123 834 000 > Php 30 000 000

ANSWER

: 20 MILLION TODAY