Practice Math Questions Flashcards
An Institution has an F&A rate (MTDC) of 40%. The total cost of the award received by Dr. Sanchez is $500,000 with no exclusions. What are the total indirect costs for the project?
a. $200,000
b. $357,143
c. $142,857
d. $312,500
c. $142,857
Explanation: The total award amount is the sum of the total direct costs and the total indirect costs. The total indirect costs are determined by multiplying the direct costs by the indirect costs rate in this example since there are no exclusions. This gives us the equation: Total Award Costs = Total Direct Costs
+ (Total Direct Costs * 40%). Rearranging this equation gives us: Total Award Costs / 1.40 = Total Direct Costs. Plugging numbers in, we get $357,143. From there, we need to multiply by 40% to receive the total indirect costs.
Dr. Kim has received an award with $125,000 available in direct costs. $25,000 of that is Materials and Supplies. The F&A rate (MTDC) is 61%. What are the TOTAL costs for the project?
a. $201,250
b. $77,639
c. $161,000
d. $186,000
a. $201,250
Explanation: This is a sneaky red herring problem. Even though it gives you to Materials and Supplies costs, you don’t need to know that at all since the indirect rate is modified total direct costs and Materials and Supplies costs aren’t excluded in MTDC cost calculations. Thus, all you have to do multiply the total direct costs by the indirect rate, then add that number back to total direct costs: $125,000 * 0.61 = $76,250 + $125,000 = $201,250.
Dr. Martin’s award has $400,000 available in Total Costs. Of the total costs, there is $10,000 in equipment, $20,000 for the first sub, and $75,000 for the second sub. The indirect cost rate is 30% MTDC. What is the Modified Total Direct Costs for this award?
a. $261,538
b. $295,000
c. $340,000
d. $307,692
a. $261,538
Explanation: Recall that equipment and any amount over the first $25,000 for subs is excluded from direct cost when calculating modified total direct costs. In this example, you will exclude $10,000 for equipment and $50,000 for the second sub ($75,000 total sub costs ‐ $25,000 allowed in MTDC calculation = $50,000 excluded). From there, divide the total by (1 + indirect cost rate) to get the MTDC total. $400,000 – ($10,000 + $50,000) = $340,000 / 1.30 = $261,538
An Institution wants to re‐budget $20,000 from equipment into salary and fringe for an award with total costs of $750,000. The indirect cost rate is 50% MTDC, and the fringe rate is 30%. How much will be available for salary; how much for fringes?
a. $13,333; $3,999
b. $15,385; $4,615
c. $10,256; $3,077
d. $15,385; $7,692
c. $10,256; $3,077
Explanation: The indirect rate is MTDC in this example, so we know that indirect wasn’t initially charged on the equipment costs, but it will be charged on the salary and fringe. This means we won’t have the full $20,000 to work with as a portion of it will now be charged to indirect due to this move. The total amount we’ll have for salaries and fringes will be: $20,000 / 1.50 = $13,333.
From here, you can determine the salary using the following equation: $13,333 / 1.30 = $10,256. The fringe total is determined by multiplying that amount by the fringe rate: 10,256 * 30% = 3,077.
You are working with Dr. Agah to create an NIH Modular Budget. So far, your budget includes the following direct costs: $100,000 in salaries and fringes for all personnel, and $15,000 for equipment. How much more can you budget in direct costs to reach the next module?
a. $25,000
b. $10,000
c. $0
d. $35,000
b. $10,000
Explanation: NIH Modules occur in $25,000 increments. Since you’ve already budgeted $115,000 in direct costs, you only need $10,000 more in direct costs to reach the next increment of $125,000.
You are working with Dr. Agah to create an NIH Modular Budget. So far, your budget includes $125,000 in total direct costs. Dr. Agah now wants to add a subcontractor with total cost of $100,000, and a 25% MTDC indirect rate with no exclusions. After this addition, what are the total modular direct costs on the budget?
a. $225,000
b. $200,000
c. $125,000
d. $205,000
d. $205,000
Explanation: For Modular Budgets, you must subtract the subcontractor’s (also known as a consortium partner’s) indirect costs from the total direct costs to find the total modular direct cost. Find the Subcontractor’s total indirect cost using $100,000 total costs / 1.25 = $80,000 total direct costs;
$100,000 total cost ‐ $80,000 total direct costs = $20,000 total indirect costs.
($125,000 total prime direct costs + $100,000 total sub costs) ‐ $20,000 total sub indirect costs =
$205,000 total modular direct costs
Another way to consider this is the total modular direct costs are the sum of the total direct costs for the prime and the sub, this changes the final equation to: $125,000 total prime direct costs + $80,000 total sub direct costs = $205,000 total modular direct costs
Dr. Zhang’s award has $500,000 available in Total costs. Of the total costs, there is $10,000 in equipment, $20,000 for the first sub, and $75,000 for the second sub. The indirect cost rate is 30% TDC. What is the Total Direct Costs for this award?
a. $338,461
b. $303,846
c. $395,000
d. $384,615
d. $384,615
Explanation: No exclusions are needed since this is asking for total direct costs and not modified total direct costs. The equation is $500,000 / 1.30.
Dr. Baldera wants to apply to a DOE ARPA-E program that requires cost share. If the total costs requested from ARAP-E are $650,000, what amount of cost share must be budgeted to meet a cost share requirement of 20% of total project cost?
a. $130,000
b. $162,500
c. $108,333
d. $520,000
b. $162,500
Explanation: In order to calculate cost share as a percentage of total project cost, use this equation: (Total Costs Requested / (1 – cost share percentage)) = Total Project Costs – Total Costs Requested = Total Cost share amount.
Note, answer A is the answer if you were asked to calculate cost share as 20% of total requested cost. That equation is: Total Costs Requested * Cost Share Percentage = total cost share amount.
Dr. Matherson’s institutional base salary is currently $209,821 each academic year. Assuming that the Executive Pay Level II is currently capped at $203,700, what is the maximum amount of Dr. Matherson’s salary that is allowed to be charged to a National Institutes of Health (NIH) project during the academic year in year 1.
a. $56,046
b. $203,700
c. $152,775
d. None of the above
c. $152,775
Explanation: One thing to remember with NIH’s salary cap is that the executive pay level is for a calendar year (or 12-month) appointment, not an academic year (or 9-month) appointment. Thus, you must convert that amount from calendar year to academic year to solve this project. You can do this with the following equation: (CY amount / 12 months in CY) * 9 months in AY = Max AY salary cap amount.
This question is a bit of a sneaky red herring in that you don’t need to know Dr. Masterson’s salary itself to solve the question.
A project budget includes $500,000 in total direct cost, of which $10,000 is for equipment, and $25,000 is for tuition. What amount is allowed to be requested as indirect if the budget is required to follow NIFA’s 30% TFFA indirect policy?
a. $164,285
b. $150,000
c. $139,500
d. $214,285
d. $214,285
Explanation: Recall that TFFA means “total federal funds awarded.” Total federal funds awarded is just another way to say “total project costs.” This means that the indirect is actually 30% of the total project costs, not the total direct costs. Determining this is very similar to how we determined cost share as a percentage of total project costs that is shown above. The equation is: (Total Direct cost / (1 – TFFA percentage)) = Total Project Costs – Total Direct Costs = Total indirect cost.
Note that TFFA calculations require that you look at the total direct costs, so you should not calculate MTDC at all to answer this question.
A PI receives a grant of $300,000 from NIH. It is on an MTDC basis with no exclusions from the IDC base. The institution’s IDC rate is 56%. What are the total direct costs?
a. $56,000
b. $300,000
c. $192,308
d. $107,692
c. $192,308
The NIH salary cap is set at $212,100. You are building a budget for a project with two PIs. PI 1 has a 12-month salary of $250,000 with a fringe benefits rate of 32%, and PI 2 has a 9-month salary of $160,000 with a fringe benefits rate of 30%. They will both work on the project for 1 calendar month each year. With an institutional IDC rate of 59% and no escalations, what is the total cost for the two PIs for a five-year project period?
a. $369,215
b. $368,153
c. $73,631
d. $323,281
b. $368,153
Solution strategy:
Step 1: PI 1’s salary is over the cap. The salary for the one month on the project is
$212,100 / 12 = $17,675. Including 32% f/b, the direct costs are $23,331.
Step 2: PI 2’s salary is also over the cap, because the monthly compensation is
$160,000 / 9 = $17,778 which is higher than the monthly cap rate of $17,675. Therefore, PI 2 will also have $17,675 on the project for the one month of work. Including 30% f/b, the direct costs are $22,977.50.
Step 3: Add the salaries with f/b and apply IDC: $73,630.52
Step 4: Multiply by 5 for the five year project period: $368,152.58 -> round to $368,153
A foundation sponsors a PI’s research with a $200,000 grant on a TDC basis. The PI budgeted for $30,000 in equipment and $9,500 in foreign travel. What are the indirect costs if the IDC rate is 15%?
a. $30,000
b. $25,500
c. $24,075
d. $26,087
d. $26,087
A PI is rebudgeting $40,000 in participant support costs into equipment, with sponsor approval. If the institution’s IDC rate is 64% MTDC, how much money will be available for equipment?
a. $24,390
b. $65,600
c. $64,000
d. $40,000
d. $40,000 - both categories do not carry IDC under an MTDC base
You are helping a PI with a budget draft for a project with a total costs limit of $400,000 on an MTDC basis. Your institution’s IDC rate is 63%. The PI needs $175,000 in personnel costs and $20,000 in travel. How much can you budget for equipment?
a. $82,150
b. $50,399
c. $125,767
d. $57,000
a. $82,150 - total costs for personnel and travel are ($175,000+$20,000)*1.63 = $317,850
