Can ≠ Should

Dodong tells an interesting story. A local bank has been bugging him, through several text messages and phone calls, to avail himself of its credit-to-cash arrangement. This means that Dodong can convert the available limit of his credit card to cash. He will just pay a certain amount per month for 36 months at a “low” monthly add-on rate of 0.59 percent.

As an added incentive, Dodong could pay his first monthly installment 60 days (two months) after he gets the money. Dodong’s credit-card statement cutoff is every fifth of the month. If he receives the loan proceeds before July 5, then his credit-card statement covering June 6 to July 5 will be Month zero, and it should reflect the credited amount. In the next statement covering July 6 to August 5 (Month one), no installment payment will be due, yet. It is in the succeeding statement covering August 6 to September 5 (Month two) that the first installment payment due will be reflected. The last installment payment due will be reflected in Dodong’s statement covering July 6, 2022 to August 5, 2022 (Month 37).

Dodong also finds out that the bank has approved the expansion of his credit limit to P189,974. Dividing P189,974 by 36 months yields P5,277.06 per month. The monthly add-on interest rate of 0.59 percent is multiplied to the principal amount of P189,974 to get P1,120.84. So, every month for 36 months, Dodong should be paying P5,277.06 + P1,120.84 = P6,397.90.


Thanks to Microsoft Excel, Dodong is able to compute for the internal rate of return (IRR) of cash flows. On cell A1, Dodong types “Month,” and then on cell B1, he types “Cash Flow.” Cells A2 to A39 should contain the month numbers (zero to 37). Cell B2 should contain the total loan amount, which is P189,974 (Month zero). Cell B3 should contain 0, since no payment is due yet in Month one. Cells B4 to B39 should each contain P6,397.90, which is the monthly installment payment for 36 months (Months two to 37). On some other cell—say, D1—Dodong types in this formula: =IRR(B2:B39).

It turns out that the IRR, or the effective monthly interest rate, is about 1.02 percent—almost double the 0.59 percent monthly add-on interest rate. It gets more interesting when Dodong tries to compute for the effective annual interest rate. On a scientific calculator, he just types in ((1+0.0102)^12)−1, and the result is about 12.95 percent. In other words, Dodong would effectively be paying 12.95 percent interest per year.

Now, if Dodong decides to invest the proceeds, the annual return on investment should be greater than 12.95 percent for him to simply break even. So, if the ROI is 15 percent, should Dodong be happy? No, because he knows that the 91-day T-bill offers a risk-free rate of 4.453 percent. Assuming 360 days in a year, the effective annual interest rate of the T-bill is computed as follows: ((1+0.0102)^(360/91))−1. That is roughly 18.81 percent. Assuming 365 days in a year, the effective annual interest rate is roughly 19.09 percent. So, for Dodong to be happy, he should invest the proceeds in an instrument that gives him a rate greater than the sum of the breakeven rate (12.95 percent) and the risk-free hurdle rate (18.81 percent or 19.09 percent, depending on how many days are assumed to be in a year). In short, Dodong’s required ROI should be at least 33 percent!

Dodong gathers that the year-to-date growth rate of the Philippine Stock Exchange Index is about 7 percent. Its compound annual growth rate over the last four years is about 1 percent. Over the last five years, the CAGR is about 3 percent. Over the last 10 years, the CAGR is about 16 percent. So, over three years (36 months), if the loan proceeds were to be invested in the Philippine stock market, it would probably be difficult to grow the money faster than its effective annual interest rate plus the hurdle rate posed by a 91-day T-bill.

It is also interesting to note that the gross annual interest rate on Dodong’s savings account with the same bank is just 0.25 percent. If he also considers the withholding tax, then the interest rate on his savings account is effectively just 0.20 percent. 13.76 percent versus 0.20 percent—What a huge spread that is! People should no longer wonder why banking has been such a profitable business in this country!

So, it looks like Dodong will not be biting the bank’s offer. He does not have any productive use for the money anyway. That he can readily borrow money does not mean that he should. Dodong is a wise fellow.

Dr. Ser Percival K. Peña-Reyes teaches economics at the Ateneo de Manila University.

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  1. Okay, I would be the first to admit that there are a few errors spotted in this article version submitted to the press. Allow me to rectify these errors here.

    1. “Now, if Dodong decides to invest the proceeds, the annual return on investment should be greater than 12.95 percent for him to simply break even. So, if the ROI is 15 percent, should Dodong be happy? No, because he knows that the 91-day T-bill offers a risk-free rate of 4.453 percent. Assuming 360 days in a year, the effective annual interest rate of the T-bill is computed as follows: ((1+0.0102)^(360/91))−1. That is roughly 18.81 percent. Assuming 365 days in a year, the effective annual interest rate is roughly 19.09 percent. So, for Dodong to be happy, he should invest the proceeds in an instrument that gives him a rate greater than the sum of the breakeven rate (12.95 percent) and the risk-free hurdle rate (18.81 percent or 19.09 percent, depending on how many days are assumed to be in a year). In short, Dodong’s required ROI should be at least 33 percent!”

    The formula should be ((1+0.04453)^(360/91))−1, but this is still wrong because the quoted 91-day T-bill rate is already annualized. The correct way to compute for the effective 91-day interest rate would be: r = ((1+0.04453)^(91/360))-1 = 0.011073639 = 1.1074%, or r = ((1+0.04453)^(91/365))-1 = 0.010921120 = 1.0921% (depending on how many days are assumed to be in a year). So, ((1+0.011073639)^(360/91))−1 = ((1+0.010921120)^(365/91))−1 = 0.04453 = 4.453%, which is the quoted (annualized) 91-day T-bill rate.

    To avoid confusion, we can just use the 364-day T-bill rate, which is about 5.87 percent. So, if the loan proceeds were to be invested, the annual return on investment (ROI) should be greater than the sum of the cost recovery rate (12.95 percent) and the risk-free hurdle rate (5.87 percent). In short, the required annual ROI is at least 18.82 percent, not 33 percent as originally computed. Still, the key message is the same: It would be difficult to grow the money faster than its effective annual interest rate plus the hurdle rate posed by a 364-day T-bill.

    2. “It is also interesting to note that the gross annual interest rate on Dodong’s savings account with the same bank is just 0.25 percent. If he also considers the withholding tax, then the interest rate on his savings account is effectively just 0.20 percent. 13.76 percent versus 0.20 percent—What a huge spread that is! People should no longer wonder why banking has been such a profitable business in this country!”

    The comparison should be 12.95 percent versus 0.20 percent. This is just a minor typographical error. Still, the point is that the bank is enjoying a glaringly huge interest rate spread.

    I have already written an erratum that should be included in next week’s article. Notwithstanding these corrections, though, the main message of my article remains the same. It still might be good for Dodong to decline the bank’s offer if he knows that he does not have any productive use for the money. That he can readily borrow money does not mean that he should. Dodong knows that there is a cost to borrowing money that one must recover, and, on top of that, there is a risk-free rate of return that must be hurdled. Indeed, Dodong can demonstrate wisdom by not being an impulsive borrower.

  2. Here is the edited version that I wanted to submit to the press:

    Can ≠ Should

    Dodong tells an interesting story. A local bank has been bugging him, through several text messages and phone calls, to avail of its credit-to-cash arrangement. This means that Dodong can convert the available limit of his credit card to cash. He will just pay a certain amount per month for 36 months at a “low” monthly add-on rate of 0.59 percent.

    As an added incentive, Dodong could pay his first monthly installment 60 days (two months) after he gets the money. Dodong’s credit card statement cutoff is every fifth of the month. If he receives the loan proceeds before August 5, then his credit card statement covering July 6 to August 5 will be Month 0, and it should reflect the credited amount. In the next statement covering August 6 to September 5 (Month 1), no installment payment will be due yet. It is in the succeeding statement covering September 6 to October 5 (Month 2) that the first installment payment due will be reflected. The last installment payment due will be reflected in Dodong’s statement covering August 6, 2022 to September 5, 2022 (Month 37).

    Dodong also finds out that the bank has approved the expansion of his credit limit to P189,974.00. Dividing P189,974.00 by 36 months yields P5,277.06 per month. The monthly add-on interest rate of 0.59 percent is multiplied to the principal amount of P189,974.00 to get P1,120.84. So, every month for 36 months, Dodong should be paying P5,277.06 + P1,120.84 = P6,397.90.

    Thanks to Microsoft Excel, Dodong is able to compute for the internal rate of return (IRR) of cash flows. On cell A1, Dodong types “Month”, and then on cell B1, he types “Cash Flow”. Cells A2 to A39 should contain the month numbers (0 to 37). Cell B2 should contain the total loan amount, which is 189,974.00 (Month 0). Cell B3 should contain 0, since no payment is due yet in Month 1. Cells B4 to B39 should each contain −6,397.90, which is the monthly installment payment for 36 months (Months 2 to 37). On some other cell—say, D1—Dodong types in this formula: =IRR(B2:B39).

    It turns out that the IRR, or the effective monthly interest rate, is about 1.02 percent—almost double the 0.59 percent monthly add-on interest rate. It gets more interesting when Dodong tries to compute for the effective annual interest rate. On a scientific calculator, he just types in ((1+0.0102)^12)−1, and the result is about 12.95 percent. In other words, Dodong would effectively be paying 12.95 percent interest per year.

    Now, if Dodong decides to invest the proceeds, the annual return on investment (ROI) should be greater than 12.95 percent for him to simply recover the cost of the borrowed money. So, if the ROI is 15 percent, should Dodong be happy? No, he should not be happy, if he knows that there is a 364-day T-bill that offers a risk-free rate of about 5.87 percent. For Dodong to be happy, he should invest the proceeds in an instrument that gives him a rate greater than the sum of the cost recovery rate (12.95 percent) and the risk-free hurdle rate (5.87 percent). In short, Dodong’s required annual ROI is at least 18.82 percent.

    Dodong gathers that the year-to-date growth rate of the Philippine Stock Exchange Index is about 7 percent. Its compound annual growth rate (CAGR) over the last four years is about 1 percent. Over the last five years, the CAGR is about 3 percent. Over the last ten years, the CAGR is about 16 percent. So, over three years (36 months), if the loan proceeds were to be invested in the Philippine stock market, it would probably be difficult to grow the money faster than its effective annual interest rate plus the hurdle rate posed by a 364-day T-bill.

    It is also interesting to note that the gross annual interest rate on Dodong’s savings account with the same bank is just 0.25 percent. If he also considers the withholding tax, then the interest rate on his savings account is effectively just 0.20 percent. 12.95 percent versus 0.20 percent—What a huge spread that is! People should no longer wonder why banking has been such a profitable business in this country!

    So, it looks like Dodong will not be biting the bank’s offer, since he admits that he does not have any productive use for the money anyway. That he can readily borrow money does not mean that he should. He knows that there is a cost to borrowing money that one must recover, and on top of that, there is a risk-free rate of return that must be hurdled. Indeed, Dodong has demonstrated wisdom by not being an impulsive borrower.

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