Friday, September 12, 2008

Thanks to my commentators and pop quiz

Hi folks, it's been a while. While I reserve the right to post as I please, and you the right to avoid reading this, sheer courtesy obliges me to be timely in moderating comments. Actually I would have wanted to turn the moderation option off, except that spammers have a field day. So I have now dealt with the commentary backlog, and thanks for paying attention. And since you are, I have a pop quiz (and perhaps this should be standard interview question for financial analysts): the newspaper today reports that the debt of the Republic of the Philippines stands at Php 3.964 trillion, of which 2.303 trillion is local and the rest is domestic. Averaging over the number of Filipinos, every citizen owes Php43,805.

Estimate the net present value of the average debt burden of each individual today. List all the assumptions and calculations.

Hint: it is is certainly less than 43,805!

2 comments:

Ser Percival K. Peña-Reyes said...

ASSUMPTIONS

1. Suppose that I expect to pay off my share of the national debt burden during this lifetime (say, during my 40 productive years from age 20 to age 60).
2. I put some money into an investment vehicle that earns 6% annually, net of tax. I shall use the future proceeds to pay off my share of the national debt burden.
3. Suppose that after working for 40 years, my investment will grow to P43,805.00, which is given as the average debt burden of each individual today.

COMPUTATION

To get the present value of P43,805.00 at 6% annual interest over 40 years, apply the formula: FV = PV(1+r)^t, where FV = future value, PV = present value, r = interest rate, t = time. Using algebra, we get: PV = FV/(1+r)^t.

So, we proceed as follows:

PV = P43,805.00/(1+0.06)^40
PV = P43,805.00/10.28571794
PV = P4,258.82

So, to have enough money to pay off the P43,805.00 I owe to the government, I must invest P4,258.82 today and leave it to grow at 6% yearly during my 40-year productive period.

Orlando Roncesvalles said...

Ok, you said "net" PV. That means you have to account for the income stream from the fact that the State owns certain resources -- roads, mountains, foreign exchange of the central bank, oil or gas in the ground. Surely, the value of all that must have an income stream greater than $60 per resident, which would even out the debt of somewhat less than $1,000 (assuming 6% discount rate). The resident is in fact "ahead" and not behind, so there is no net debt that needs to be paid off. Hence, net PV of debt is probably negative.