Saturday, April 21, 2018

The Cost of Eliminating Subsidized Loans to Students

A Financial Model on Costs to Students from
Eliminating Student Loan Subsidies

Introduction:   Currently, low-income undergraduate students can take out a total of $31,000 in federal student loan.  Subsidized student loans are only available to people in low-income households.  The main difference between subsidized and unsubsidized student debt is that the government pays all interest costs on subsidized debt when the student is in school while interest accrues on unsubsidized loans. 

 The current limit on subsidized student loans is $23,000.  The total limit on undergraduate federal student loans is $31,000.

The Trump Administration is proposing to eliminate all subsidized student loans.

The purpose of this post is to model and analyze the  impact of this policy change for a student who is planning to take full advantage of subsidized student loans.  I also examine how this financial cost depends on the number of years it takes for the student to graduate.

Methodology:   I set up a spread sheet where the key model inputs are number of years it takes for a student to graduate, the interest rate on the student loan, and the maturity of the student loan.

Key Assumptions:

 In this model, I assume the student borrows $31,000/n each year where n is the number of years it takes for the student to graduate.  When subsidized loans exist the annual total borrowed for subsidized loans is $23,000/n and total unsubsidized loans for the course of the person’s undergraduate career is $8,000.

 (An expanded version of this model will consider uneven borrowing scenarios, where student borrows a different amount each year or perhaps drops out from school for a few years.)

Student remain in deferment until six month after graduation or leaving school.  

Student does not apply for loan deferments for economic hardships or when unemployed.

The interest rate is 5 percent.

Student loan maturity is 20 years.

The procedure to calculate lifetime costs involves two steps.

Step One: Calculate the total loan balance on the day the student borrower starts repayment.  The subsidized loan at time of repayment is equal to the balance when issued since all interest is paid for. The FV of the unsubsidized loan is determined at time of graduation and multiplied by (1+0.05)0.5 to account for the six-month delay in repayment after graduation.

Inputs of FV function:

INT interest rate 0.05 or some other assumption.

NPER number of periods in this case number of years in school. 

PMT is payment in this case the annual loan amount.

PV in this case 0

Type is ! for end of period.

The FV gives the value of the loan at graduation.   Repayment is six months later.   The value of the loan at repayment is FV0.5

The total loan balance is the sum of the subsidized and unsubsidized loan balance at time of repayment.

Step Two:  Calculate total payments over the lifetime of the loan.  This is done by using PMT function to get monthly payment and then multiplying by the total number of payments.

Spreadsheet for person who graduates in four years:

Subsidized Loans
No Subsidized Loans
Date of First Loan Payment
Subsidized Loan
Unsubsidized Loans
Interest Rate
Number of years In school
Date Repayment Starts
FV of subsidized loans
FV of unsubsidized Loans
Total Loans
Loan Maturity
Loan PMT
Lifetime Payments

·      The elimination of subsidized loans increases lifetime repayment costs of the loan by $5,805 when the person graduates in four years and starts repayment six months after graduation.  (The other key assumptions are a 5% student loan interest rate and a 20-year student loan.)

Impact of delays in finishing schools:

The addition cost stemming from the loss of the subsidy can be obtained by changing line 6 of the spreadsheet number of years in school.   Below we present results for # of years in school for 4, 5, and 6. 

Calculations are below:

# of Years in School
Payments with Subsidized Loans
Payments with No Subsidies

·      The elimination of subsidized loans leads to even higher costs for the person who spends more years in school.   Additional lifetime costs of loans are $6,887 for the person who graduates after 5 years and $8,005 for the person who graduates after six years.

Authors Note:  I will soon create additional Excel Finance problems involving the elimination of subsidized student loans.   The problems will involve students who borrow different amounts each year, take some time off from school, or obtain additional loan deferments to obtain graduate school.  

This problem is question 17 on the Excel finance tutorial.