Finding Grant Element using the Jie Chen 2005 Method for Calculating NPV of the Loan

To qualify as official development assistance (ODA), development loans must have a grant element of at least 25 percent, calculated using a stated annual interest rate of 10 percent. Your colleague and former ADMS 4540 student just started work as a policy analyst in Canadas Ministry of Foreign Affairs and is discussing some of the work she has been doing recently with you over lunch. She tells you about a recent meeting with representatives from Mongolia to discuss development assistance which Canada wishes to extend to the country. The assistance will have the following characteristics: a $75 million loan, to be amortized over 10 years by 20 semi-annual payments, after a grace period of 5 years during which only interest would be paid semi-annually. Canada would charge interest at a stated annual rate of 7%. Calculate the grant element of this loan.

Now lets calculate the grant element of this loan using the method another former ADMS 4540 student (and BAS graduate) Jie Chen discovered back in 2005. First find the payments for an unsubsidized loan using a stated annual interest rate of 10 percent, following the usual grace period of 5 years. That is, calculate the interest-only payments at 5% semi-annually for the first 5 years and then amortize the $75 million over 10 years by 20 semi-annual payments at 5% semi-annually. Next, calculate the payments at a subsidized annual rate of 7%. Take the difference of each payment which is the subsidy each period over 15 years (or 30 semi-annual periods) and find the PV of these subsidies. Compare your result with the grant element you calculated earlier. How do they compare? Unlike finding the NPV of a corporate loan, the Jie Chen 2005 method does not appear to involve less calculation in ODA problems. Why?